Question

Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year. Find when the sale of cars will be more then the sale of motorcycles.

Answer 1

Final answer is approx 6.644 years.

Explanation:

Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.

So we can use growth formula:

`A=P\left(1+r\right)^t`

Then we get equation for motorcycles and cars as:

`A=5.75\left(1+0.16\right)^t`

`A=3.5\left(1+0.25\right)^t`

Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:

`3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t`

`3.5\left(1.25\right)^t>5.75\left(1.16\right)^t`

`3.5\left(1.25\right)^t>5.75\left(1.16\right)^t`

`(\left(1.25\right)^t)/(\left(1.16\right)^t)>(5.75)/(3.5)`

`\left((1.25)/(1.16)\right)^t>1.64285714286`

`t\cdot\ln\left((1.25)/(1.16)\right)>\ln\left(1.64285714286\right)`

`t>(\ln\left(1.64285714286\right))/(\ln\left((1.25)/(1.16)\right))`

`t>6.6436473051`

Hence final answer is approx 6.644 years.