The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months), with corresponding to January. Determine the months when sales exceed units at any time during the month.
A)July through May
B)April through August
C)April through July
D)May through July
E)June through August

Question

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by  where t is the time (in months), with  corresponding to January. Determine the months when sales exceed  units at any time during the month.
A)July through May 
B)April through August 
C)April through July 
D)May through July 
E)June through August

Quizplus · Accepted Answer

To determine when sales exceed 150 units (11eb80b1_afba_7015_a291_8b19c56ee2ce_TB8633_11 in hundreds), we can set the equation equal to 150 and solve for t.
11eb80b1_afba_7013_a291_e5e380bdc2dd_TB8633_11 > 150 
ln(t + 2) > ln(150/11)
t + 2 > e^(ln(150/11))
t + 2 > 3.04
t > 1.04
Thus, sales exceed 150 units at any time during the month for t values greater than 1.04 months. Since January corresponds to t = 0, this means sales exceed 150 units at any time during the month in February through July. The answer is therefore D, May through July.

The Monthly Sales S (In Hundreds of Units) of Baseball