Madison is taking over as Chief Marketing Officer at MidWest Graphics.She has pledged to increase sales from their current level of $12,000,000 at a rate of 10% per year until the firm hits sales of $20,000,000 per year.How long will it take Madison to hit the target goal at this rate of increase?
A)7.67 years
B)1.53 years
C)5.36 years
D)At that rate,Madison will never reach the target sales level in her lifetime.

Question

Quizplus · Accepted Answer

To solve this problem, we can use the formula for exponential growth:

P = P0*(1 + r)^t

where:
P0 = initial sales level = $12,000,000
P = target sales level = $20,000,000
r = annual growth rate = 10% = 0.1
t = number of years

Substituting the values, we get:

$20,000,000 = $12,000,000*(1 + 0.1)^t

Simplifying the equation, we get:

1.6667 = 1.1^t

Taking the logarithm of both sides, we get:

log(1.6667) = t*log(1.1)

t = log(1.6667)/log(1.1)

t = 5.36 years (rounded to two decimal places)

Therefore, it will take Madison 5.36 years to hit the target sales level of $20,000,000 per year at a rate of 10% per year. The correct answer is C.

Madison Is Taking Over as Chief Marketing Officer at MidWest