Question

1. There are 300 bacteria in a culture, and the number of bacteria quadruples every 5 hours.

A. Write a function, N, that gives the number of bacteria t hours from now.

B. How many will there be in 20 hours?

C. In how many hours will there be 2,000 bacteria?

2. The population of Johnsonville was 900 in 1880 and is known to double every 20 years.

a. Write a function, P, that gives the population y years after 1840.

b. If this model is accurate, what is the population in 2010?

c. In what year did the population first exceed 5000?

3. A population increases by 5.5% per year. In how many years will the population triple?

4. An investment involving a single deposit pays 6% per year, compounded annually. What deposit is needed to have $30,000 after 20 years?

Answer 1

(1)

(A)

we can use formula

we are given

now, we can plug it back

(B)

we can plug t=20

............Answer

(C)

we can set

N(t)=2000

and then we can solve for t

we can take ln on both sides

............Answer