Solve the problem.
-A company estimates that it will sell N(t) hair dryers after spending $t thousands on advertising as given by: For which values of t is the rate of sales N'(t) in creasing?

Question

Solve the problem.
-A company estimates that it will sell N(t) hair dryers after spending $t thousands on advertising as given by:  For which values of t is the rate of sales N'(t) in  creasing?
A) 40 < t < 50 
B) 50 < t < 60 
C) 40 < t < 60 
D) t > 40

Quizplus · Accepted Answer

To determine when the rate of sales, N'(t), is increasing, we need to find where the second derivative of N(t) with respect to t, N''(t), is greater than zero. Taking the second derivative of N(t), we get N''(t) = 12.96e^(0.4t) which is always greater than zero for all t. Therefore, N'(t) is increasing for all t, so we need to find the values where N'(t) is positive. From the given expression for N'(t), we can see that N'(t) will be positive if (0.4t - 6.48) > 0, or equivalently, if t > 16.2. Thus, N'(t) is increasing for t values greater than 16.2. The only answer choice that satisfies this condition is A) 40 < t < 50, so it is the best choice.

Solve the Problem. -A Company Estimates That It Will Sell N(t) Hair Dryers