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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.

Respuesta :

Answer: The fraction would be 0.53.

Step-by-step explanation:

Since we have given that

[tex]r(t)=A.(1.05)^t[/tex]

where, A is the constant initial production rate

t is the time.

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

[tex]r(98)=A.(1.05)^{98}\\\\r(98)=A.119.27[/tex]

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

[tex]r(98-13)=r(85)=A.(1.05)^{85}\\\\r(85)=A.63.25[/tex]

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

[tex]\dfrac{r(85)}{r(98)}=\dfrac{63.25}{119.27}=0.53[/tex]

Hence, the fraction would be 0.53.

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