Can someone please help me solve these both? Thanks! (: Need within 30 min **Cell Growth Under Specific Conditions**Under certain conditions, the number of diseased cells $ N(t) $ increases at a rate:\[ \frac{dN}{dt} = kN \]where $ A $ is the rate of increase at time $ t = 0 $ (in cells per day) and $ k $ is a constant.### Tasksa. **Derive a Formula** - Find a formula for the number of cells after $ t $ days, given that 300 cells are present at $ t = 0 $.\[ N(t) = \]**(Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)**b. **Calculate After 8 Days** - After 8 days, there are [ ] diseased cells present. - Use the answer from part a to find this answer. Round to the nearest whole number as needed.### Instructions- Enter your answer in each of the answer boxes. ### Understanding Marginal Profit in Cheese SalesThe marginal profit in dollars on Brie cheese sold at a cheese store is given by the function:\[ P'(x) = x (60x^2 + 30x) \]where $ x $ represents the amount of cheese sold, in hundreds of pounds. The initial profit is $- $20$ when no cheese is sold.#### Tasks:**a. Find the Profit Function**Determine the profit function $ P(x) $.**b. Calculate the Profit from Selling 400 Pounds of Brie Cheese**Evaluate the profit from selling 400 pounds of Brie cheese.#### Instructions:1. Solve for the profit function $ P(x) $. - Enter the solution in the provided answer box.2. Calculate the specific profit for 400 pounds of Brie cheese. - The answer should be placed in the box labeled with a dollar sign $\$ $.\[ \text{Enter your answer in each of the answer boxes.} \]

Name: Can someone please help me solve these both? Thanks! (: Need within 30
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Can someone please help me solve these both? Thanks! (: Need within 30 min **Cell Growth Under Specific Conditions**Under certain conditions, the number of diseased cells $ N(t) $ increases at a rate:\[ \frac{dN}{dt} = kN \]where $ A $ is the rat

Rate at which number of diseased cells N(t) are increasing at time t is given by N'(t)=Aekt. Integrate the equation for the rate of change ∫N'(t)dt=A∫ektdtN(t)=Akekt+c (a) Substitute 40 for A, 3 for t and 200 for N'(t) in the equation N'(t)=Aekt. 200=40ek×65=e6kln5=6kk=ln56 Substitute 0 for t, 300 for N(0), and ln56for k in the equation N(t)=Akekt+c to determine c. 300=40×6ln5eln56(0)+c300=240ln5+cc=300-149.120c=150.88 Substitute 150.88 for c,ln56 for k and 40 for A in the equation N(t)=Akekt+c. N(t)=40×6ln5eln56t+150.88. therefore the equation is N(t)=40×6ln5eln56t+150.88.(b)' Substitute 8 for t in the equation N(t)=40×6ln5eln56t+150.88. N(8)=40×6ln5eln56(8)+150.88=149.120 e2.145+150.88=1424.66 Therefore the population of cells after 8 days is 1424.66.Second question: (a) The profit function is determined on integrating the function representing the rate of change. ∫p'(x)dx=∫x60x2+30xdxp(x)=∫60x3+30x2dxp(x)=60x44+30x33+cp(x)=15x4+10x3+c Substitute 0 for x and -20 for p(0) to determine the value of c. p(0)=0+k-20=k Therefore the profit function is: p(x)=15x4+10x3-20 (b) Substitute 4 for x in the equation p(x)=15x4+10x3-20 to determine the profit. p(4)=15(4)4+10(4)3-20=3840+640-20=4460 Therefore the profit is $4460

Math

Calculus

Under certain conditions, the number of diseased cetls N(t) at time t increases at a rate N'(t) = A e kt, where A is the rate of increase at time 0 (in cells per day) and k is a constant. a. Suppose A = 40, and at 3 days, the cells are growing at a rate of 200 per day. Find a formula for the number of cells aftert days, given that 300 cells are present at t = 0. b. Use your answer from part a to find the number of cells present after 8 days. a. Find a formula for the number of cells, N(t), after t days. N(t) =| (Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.) b. After 8 days, there are cells present. (Use the answer from part a to find this answer. Round to the nearest whole number as needed.)

Under certain conditions, the number of diseased cetls N(t) at time t increases at a rate N'(t) = A e kt, where A is the rate of increase at time 0 (in cells per day) and k is a constant. a. Suppose A = 40, and at 3 days, the cells are growing at a rate of 200 per day. Find a formula for the number of cells aftert days, given that 300 cells are present at t = 0. b. Use your answer from part a to find the number of cells present after 8 days. a. Find a formula for the number of cells, N(t), after t days. N(t) =| (Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.) b. After 8 days, there are cells present. (Use the answer from part a to find this answer. Round to the nearest whole number as needed.)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: 200)** = 700

A: 20032x+2=700

Q: A car rental agency rents 210 cars per day at a rate of 31 dollars per day. For each 1 dollar…

Q: Q1: A plastic injection mould for a milk crate cost $100 000. The crate weighs 600g and the plastic…

A: To find the answers to the given questions, we'll go step by step: (a) The number of crates made…

Q: Solve for S2 within using the following: x=27.8; s²= 7.56; N₁ = 1 x₂ = 21.8; s²= 2.92; N₁ = 4 2 x =…

A: Given x¯1=27.8, s12=7.56, N1=4 x¯2=21.8, s22=2.92, N2=4 x¯3=33.5, s32=5.66, N3=4

Q: Tools / Question 7 Use the diagram to solve forz +45 145 C. 90 45

Q: Evaluate the following integral:

A: Given, ∫2416-25n2dn

Q: A student who is driving home for the holidays averages 61.5 miles per hour. Set up the problem…

A: Answer:Distance travelled by an object in a time duration is always equal to the product of speed…

Q: Is there another way to solve this without this complicated formula?

A: The number of rolls of die, The number of faces of a die

Q: 8) x2 - 14x + 74-0 A) (14 + 101} B) (-7 +5i) C) {12, 2} D) {7 +5i}

Q: Snow is falling steadily in Syracuse, NY. After 2 hours, 4 inches of snow has fallen. If it…

A: It is given that in 2 hours 4 inches of snow has fallen.

Q: Solve 1.12 x 10-11 / 2.23 x 10-12

A: The final answer is 112/223 Which is approximately 0.502242

Q: Evaluate then simplify: Stan (4p) sec (4p)dp

Q: Solve for x. x 6 4 3 x 0 = 132 4 5 - 4

A: We will solve the determinant in terms of X and then equate it to 132.

Topic Video

Question

Can someone please help me solve these both? Thanks! (: Need within 30 min

**Cell Growth Under Specific Conditions**

Under certain conditions, the number of diseased cells $ N(t) $ increases at a rate:

\[ \frac{dN}{dt} = kN \]

where $ A $ is the rate of increase at time $ t = 0 $ (in cells per day) and $ k $ is a constant.

### Tasks

a. **Derive a Formula**
- Find a formula for the number of cells after $ t $ days, given that 300 cells are present at $ t = 0 $.

\[ N(t) = \]

**(Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)**

b. **Calculate After 8 Days**
- After 8 days, there are [ ] diseased cells present.
- Use the answer from part a to find this answer. Round to the nearest whole number as needed.

### Instructions

- Enter your answer in each of the answer boxes.

### Understanding Marginal Profit in Cheese Sales

The marginal profit in dollars on Brie cheese sold at a cheese store is given by the function:

\[ P'(x) = x (60x^2 + 30x) \]

where $ x $ represents the amount of cheese sold, in hundreds of pounds. The initial profit is $- $20$ when no cheese is sold.

#### Tasks:

**a. Find the Profit Function**

Determine the profit function $ P(x) $.

**b. Calculate the Profit from Selling 400 Pounds of Brie Cheese**

Evaluate the profit from selling 400 pounds of Brie cheese.

#### Instructions:

1. Solve for the profit function $ P(x) $.
- Enter the solution in the provided answer box.

2. Calculate the specific profit for 400 pounds of Brie cheese.
- The answer should be placed in the box labeled with a dollar sign $\$ $.

\[ \text{Enter your answer in each of the answer boxes.} \]

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Research Design Formulation$

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

Josh live 1 4/5 miles from the park. So far he walked 2/3 of the distance from his house to the park. How many miles has Josh walked?
Treyvon is a lifeguard and spots a drowning child 30 meters along the shore and 70 meters from the shore to the child. Treyvon runs along the shore for a while and then jumps into the water and swims from there directly to the child. Treyvon can run at a rate of 4 meters per second and swim at a rate of 1.2 meters per second. How far along the shore should Treyvon run before jumping into the water in order to save the child? Round your answer to three decimal places.
Hello please help with question 4. Thank you
im sorry but what's the first equation/formula supposed to be. I can't quite read it/make it out.
Please show in detail step by step how you solved the problem.
Differentiate: x¹0 cos(x) A) 10x⁹ - sin(x) D) 10x - sin(x) B) -10x'sin(x) E) -10xsin(x) C) x¹0 cos(x) + 10x sin(x) F) -x¹0 sin(x) + 10x cos(x)
solve for x.
A normal blood sugar range for someone without diabetes, 2 hours after eating, is less than 140 mg/dl. James is concerned about his health and measures and records his blood sugar 4 times a day for a week. The results are in the boxplot above. What is the minimum blood sugar reading James measured?mg/dl What is the maximum blood sugar reading James measured?mg/dl Twenty-five percent of James' blood sugar readings fall below what value?mg/dl Seventy-five percent of James' blood sugar readings fall below what value?mg/dl What percent of James' blood sugar readings are between 86 and 118?
Solve for A. 1 0 5 -2 A = 1 -2 0 1 A =
show your complete solution
Please solve for x
Solve for x. a. x plus 2 and one half equals 3 and one fifth b. x minus 2 and two thirds equals five sixths