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

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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.…

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...

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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 $\$ $.

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

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