Your production manager informs you that currently the firm is producing 1,348 heating units per month but has plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month.How many months will this take?
A)16.40 months
B)15.07 months
C)14 months
D)There is not enough information to answer this question.

Question

Quizplus · Accepted Answer

The correct answer is A.The firm is currently producing 1,348 heating units per month and plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month.Let's call the number of months it will take to reach 3,000 units per month "t".We can use the formula for exponential growth to solve for t:A = P(1 + r)^twhere:A is the final amount (3,000 units per month)P is the initial amount (1,348 units per month)r is the annual growth rate (5%)t is the number of monthsPlugging in the values we know, we get:3,000 = 1,348(1 + 0.05)^tDividing both sides by 1,348, we get:2.225 = (1.05)^tTaking the logarithm of both sides, we get:log(2.225) = t * log(1.05)Solving for t, we get:t = log(2.225) / log(1.05) = 16.40 monthsTherefore, it will take the firm 16.40 months to reach 3,000 units per month.

Your Production Manager Informs You That Currently the Firm Is