Question

Brookside School started a composting program this month and composted 65 pounds of food scraps. The school plans to increase that amount by 2% every month. You can use a function to describe the amount of food scraps the school plans to compost x months from now. Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)x. h(x)=

Answer 1

The composting program at Brookside School starts with 65 pounds of food scraps and increases that amount by 2% every month. Since the increase is a percentage of the previous month's amount, we can model this situation with an exponential function.

The formula for exponential growth is given by:

\[
h(x) = a(1 + r)^x
\]

where:
- \(h(x)\) is the amount of compost after \(x\) months,
- \(a\) is the initial amount (65 pounds in this case),
- \(r\) is the rate of growth (2% or 0.02), and
- \(x\) is the number of months.

To write it in the correct form, we substitute the known values:

\[
h(x) = 65(1 + 0.02)^x
\]

This simplifies to:

\[
h(x) = 65(1.02)^x
\]

So, the function describing the amount of food scraps the school plans to compost \(x\) months from now is:

\[
\boxed{h(x) = 65(1.02)^x}
\]