Question

A culture of yeast grows at a rate proportional to its size. If the initial population is 2000 cells and it doubles after 2 hours, answer the following questions. 1. Write an expression for the number of yeast cells after t hours. Answer: P(t)= 2. Find the number of yeast cells after 7 hours. Answer: 3. Find the rate at which the population of yeast cells is increasing at 7 hours. Answer (in cells per hour):

Answer 1

Explanation:

1) We would apply the formula,

y = ab^t

Where

a represents the initial amount of yeast.

t represents the doubling time.

From the information given

a = 2000

t = 2 hours

Since after 2 hours, the population of cells doubles, then

y = 2 × 2000 = 4000

Therefore

4000 = 2000 × b^2

Dividing through by 2000, it becomes

2 = b^2

Raising both sides of the equation by 1/2, it becomes

2^(1/2) = b^2/2

b = 1.414

The equation becomes

y = 2000(1.414)^t

2) when t = 7 hours,

y = 2000(1.414)^7

y = 22604 cells

3) the rate is 22604/7 = 3229 cells per hour