Answer:
Step-by-step explanation:
Let's first find the exponential function that models the situation in year one. The exponential standard form is
[tex]y=a(b)^x[/tex] where a is the initial value and b is the growth/decay rate in decimal form. If it is growth it is added to 100% of the initial value; if it is decay it is taken away from 100% of the initial value. We are told that the number of cars in year one was 80 million, so
a = 80 (in millions)
If b is increasing by 10%, then we are adding that amount to the initial 100% we started with to give us 100% + 10% = 110% or, in decimal form, 1.1
The model for our situation is
[tex]y=80(1.1)^x[/tex] where y is the number of cars after x years goes by. We want to find the difference between years 3 and 2, so we will use our model twice, replacing x with both a 2 and then a 3 and subtracting.
When x = 2:
[tex]y=80(1.1)^2[/tex] and
y = 80(1.21) so
y = 96.8 million cars
When x = 3:
[tex]y=80(1.1)^3[/tex] and
y = 80(1.331) so
y = 106.48 million cars
The difference between years 3 and 2 is
106.48 - 96.8 = 9.68 million cars
