Answer:
[tex]y=100(1.1^t)[/tex]
Step-by-step explanation:
we know that
The exponential function is of the form
[tex]y=a(b^t)[/tex]
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
[tex]a=100\ trucks[/tex]
substitute
[tex]y=100(b^t)[/tex]
we have the point (1,110)
For t=1 year, y=110 trucks
substitute
[tex]110=100(b^1)[/tex]
solve for b
[tex]110=100b[/tex]
[tex]b=110/100=1,1[/tex]
The rate of growth is
[tex]r=b-1=1.1-1=0.10=10\%[/tex]
the exponential equation is equal to
[tex]y=100(1.1^t)[/tex]
Verify for the third point of the table
For t=2 years
[tex]y=100(1.1^2)=121\ trucks[/tex] ---->is correct
