Question

Write an equation for the exponential growth. You will still have t as a variable in the equation

Answer 1

`y=100(1.1^t)`

Explanation:

we know that

The exponential function is of the form

`y=a(b^t)`

where

y ---> the number of trucks

t ----> is the time in years

a ---> is the initial value (number of trucks for t=0)

b is the base

r is the rate

b=(1+r)

In this problem we have

`a=100\ trucks`

substitute

`y=100(b^t)`

we have the point (1,110)

For t=1 year, y=110 trucks

substitute

`110=100(b^1)`

solve for b

`110=100b`

`b=110/100=1,1`

The rate of growth is

`r=b-1=1.1-1=0.10=10\%`

the exponential equation is equal to

`y=100(1.1^t)`

Verify for the third point of the table

For t=2 years

`y=100(1.1^2)=121\ trucks` ---->is correct