Question

NEED HELP ASAP! 10 POINTS!!! The amount of a leaves on a tree changes with time. The table below shows the amount of leaves f(t) left after time t: t(days) 0 1 2 _____________________ f(t) 100 80 64 Create an exponential function that represents the relationship between f(t) and t?

Answer 1

`f(t)=100(0.8)^t`

The equation is in the format


`f(t)=ab^t`

where a is the initial value (when t=0), b is the rate of change between terms, and t is the amount of time.

Our initial value is 100. We find the rate of change by first finding the percent of change:
amount of change/original amount
= 20/100 = 0.2

This is a percent decrease, so we will subtract it from 1:
1-0.2 = 0.8

This goes in for b.