Question

A certain motorcycle manufacturer has been building motorcycles for 98 years. Over that period, production has increased steadily at an annual rate of 5%, so that the production rate, in motorcycles/year, after t years was
r(t)=A⋅1.05^t


where A is a constant representing the initial production rate. What fraction of their total production was built during the last 13 years? Your answer should be a number between 0 and 1.

Answer 1

Answer: The fraction would be 0.53.

Step-by-step explanation:

Since we have given that

$r(t)=A.(1.05)^t$

where, A is the constant initial production rate

t is the time.

For 98 years, the production rate in motorcycles per year would be

$r(98)=A.(1.05)^{98}\\\\r(98)=A.119.27$

For 13 years, the production rate in motorcycles per year would be

$r(98-13)=r(85)=A.(1.05)^{85}\\\\r(85)=A.63.25$

So, the fraction of their total production was built during the last 13 years would be

$\dfrac{r(85)}{r(98)}=\dfrac{63.25}{119.27}=0.53$

Hence, the fraction would be 0.53.