Question

F.IF.8.b Use the properties of exponents to interpret expressions for exponential functions.Question 2 of 6A study is done on the number of bacteria cells in a petri dish. Suppose that the population size Pafter t hours is given by the following exponential function.P(t) = 1500(1.07)'Find the initial population size.Does the function represent growth or decay?Ogrowth decayBy what percent does the population size change each hour?_%

Answer 1

SOLUTION

The given function is:

$P(t)=1500(1.07)^t$

To find the initial population substitute t=0 into the function:

$P(t)=1500(1.07)^0$

Calculate the value

$P(t)=1500$

Notice that as the number of hours increases the population will also increase.

Hence the function is a growth function.

The function can be written as:

$P(t)=1500(1+0.7)^t$

Therefore the population increases by 7% each hour.