Question

assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. the growth in the scale 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. shw your work

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 (1 + r)^t

Then we get equation for motorcycles and cars as:

A = 5.75 (1 + 0.16)^t

A = 3.5 (1 + 0.25)^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 (1 + 0.25)^t > 5.75 (1 + 0.16)^t

3.5 (1.25)^t > 5.75 (1.16)^t

3.5 (1.25)t . 5.75 (1.16)^t

(1.25)^t/(1.16) > 5.75/3.5

(1.25/1.16)^t > 1.64287514286

t·In (1.25/1.16) > In (1.64287514286)

t > In(1.64285714286)/In (1.25/1.16)

t > 6.6436473051

Hence final answer is approx 6.644 years.