Question

More people are purchasing food from farmers' markets around the country. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 1.71.7% every six months. If there were 74997499 farmers' markets in 2019, how many will there be in 99 years?Given the exponential growth scenario above, answer the following questions:What is the initial value, P0P0 in this problem? What is the growth factor or growth rate (as a decimal value)? What is the nn value, or number of time periods? Question Help Question 1: Read 1

Answer 1

Step 1

Given;

`\begin{gathered} Initial\text{ farmer market=P}_0=7499 \\ b=0.017 \\ n=number\text{ of time periods} \end{gathered}`

Step 2

The exponential function for the question is

`\begin{gathered} P=P_0(1+b)^n \\ P=P_0(1+0.034)^n \\ P=P_0(1.017)^n \end{gathered}`

Step 3

The initial value in this problem is;

`P_0=7499`

Step 4

The growth rate factor as a decimal will be;

`1.017`

Step 5

What is the n value or a number of time periods?

`n=18`

Step 6

How many will there be in 9 years

`\begin{gathered} P=7499(1.017)^(18) \\ P=10157.35207 \\ P\approx10157\text{ farmers' markets} \end{gathered}`