Question

help

Answer 1

@eliesaab

Answer 2

Tell me, what is exponential growth? How is it different from linear growth?

Answer 3

Usually, exponential growth is modeled as \(\color{black}{\displaystyle f(t)=a(b^t) }\),
where \(\color{black}{\displaystyle a }\) is the initial value (i.e. what you start with), and \(\color{black}{\displaystyle b }\) is the growth rate.

Answer 4

In this case \(t\) is measured in months, and \(\color{black}{\displaystyle f(t) }\) is the number of books donated after \(t\) months.

Answer 5

You are given 3 points:
\(\color{black}{{\small [1]}\quad \displaystyle (t,\,f(t))=(0,\,80) }\)
\(\color{black}{{\small [2]}\quad \displaystyle (t,\,f(t))=(1,\,100) }\)
\(\color{black}{{\small [3]}\quad \displaystyle (t,\,f(t))=(2,\,125) }\)

Answer 6

Use any of the two points that you have to solve for \(\color{black}{\displaystyle a}\) and \(\color{black}{\displaystyle b }\).
(You can do so algebraically by plugging them into \(\small\color{black}{\displaystyle f(t)=a(b^t) }\).)

Answer 7

a=80, that is the amount at t=0.
All you need, is to find b.
as @SolomonZelman suggested
use any of the equations 2 or 3 to find b in
\[
f(t)=80 b^t
\]

Answer 8

to do that, solve for b and you are done
\[
100 =80 b^1
\]

Answer 9

How much is b?

Answer 10

Once b is found, find f(8) and approximate to the nearest integer