A cell culture contains 7 thousand cells, and is 0.12t thousand cells growing at a rate of r(t) per hour. Find the total cell count after 6 hours. Give your answer accurate to at least 2 decimal places.

A cell culture contains 7 thousand cells, and is 0.12t thousand cells growing at a rate of r(t) per hour. Find the total cell count after 6 hours. Give your answer accurate to at least 2 decimal places.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter24: Percent Practical Applications

Section: Chapter Questions

Problem 35A

See similar textbooks

Related questions

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the ladder is k meters. (k=constant) Let the distance of the bottom = x m and distance of the…

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20 and S(0)=0…

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: It would be best to express length, width, and area as functions of time. I’ll set x = width, y =…

Q: A bacteria population starts with 400 bacteria and grows ata rate of r(t) = (450.268)…

Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the rate of change of length.

Q: 2. The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an…

A: Given The number of bacteria at the beginning of an experiment = 30 hourly growth rate = 1.4%

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

Q: Initially 100 milligrams of a radioactive substance were present. After 6 hours the mass had…

Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: We have to find the area of rectangle increasing

Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always two…

A: The radius is 2 times the height, the rate at which the height increases is 3 cm/s when the pile is…

Q: There are currently 250 cells in a culture and it grows ata rate proportional to its size. After one…

A: Given data: Total cells=250 After one hour=630

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: The derivative represents the rate of change. Since given that, the length of a rectangle is…

Q: Initially there was 80 milligrams of radioactive substance present. After an 8 hour period the mass…

A: From the differential equation from the given information. dPdt=kPdPP=kdt Here, the amount of…

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the length of the ladder is L.

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform thickness. If the…

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional te…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

Q: A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the…

Q: 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

Q: The top of a ladder slides down a vertical wall at a rate of 0.15m/s. At the moment when the bottom…

A: We have given; the rate of change when ladder slides down i.e 0.15m/s The rate of change when it…

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

Q: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in…

Q: The population of a community is known to increase at a rate proportional to the number of people…

Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: The top of a ladder slides down a vertical wall at a rate of 0.125m/s. At the moment when the bottom…

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: form a triangle with given information : let BC = x dxdt=0.5 AB = y dydt=-0.375 AC = z dzdt=0…

Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

Q: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

Q: A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

Q: 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard's average…

A: Given: a) A lizard accelerates from 2 m/s to 10m/s in 4 seconds. What is lizards average…

Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

Q: Helium is pumped into a spherical balloon at a constant rate of 3 cubic feet per second. How fast is…

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A cell culture contains 7 thousand cells, and is
0.12t thousand cells
growing at a rate of r(t)
per hour.
Find the total cell count after 6 hours. Give your
answer accurate to at least 2 decimal places.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

The half-life of radioactive iodine is 60 days. How much of a 50 mg sample will be left in 40 days?
The half-life of radioactive iodine is 60 days. How much of a 50-mg sample will be left in 40 days?
The half-life of magnesium-27 is 9.45 minutes. How much of a 10-mg sample will be left in 6 minutes?
The half-life of a radioactive material is about 34.2 years. How much of the material is left after 20 years?
Researchers recorded that a certain bacteria population grew from 100 to 500 in 6 hours. At this rate of growth, how many bacteria will there be 24 hours from the start of the experiment?
Researchers recorded that a certain bacteria population grew from 100 to 300 in 8 hours. At this rate of growth, how many bacteria will there be in 24 hours?
In 1906, San Francisco experienced an intense earthquake with a magnitude of 7.8 on the Richter scale. In 1989, the Loma Prieta earthquake also affected the San Francisco area, and measured 6.9 on the Richter scale. Compare the intensities of the two earthquakes.
Use the function you found in the previous exercise to find the total area burned after 5 minutes.
In 2014, Chile experienced an intense earthquake with a magnitude of 8.2 on the Richter scale. In 2014, Los Angeles also experienced an earthquake which measured 5.1 on the Richter scale. Compare the intensities of the two earthquakes.
Researchers recorded that a certain bacteria population declined from 700,000 to 400,000 in 5 hours after the administration of medication. At this rate of decay, how many bacteria will there be 24 hours from the start of the experiment?