Question

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

Answer 1

Answer:

$y=100(1.1^t)$

Step-by-step 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