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) March through September
B) April through August
C) March through August
D) August through April
E) May through September

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) March through September 
B) April through August 
C) March through August 
D) August through April 
E) May through September

Quizplus · Accepted Answer

To solve for the months when sales exceed 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 units, we need to set the expression 11eb11e8_19ae_e84e_ad38_53943324ae5d_TB4588_11 greater than 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 and solve for t:

11eb11e8_19ae_e84e_ad38_53943324ae5d_TB4588_11 > 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11

Simplifying both sides, we get:

11eb11e8_19ae_e84e_ad38_53943324ae5d_TB4588_11 - 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 > 0

Using the given expression for S, we get:

11eb11e8_19ae_e84e_ad38_53943324ae5d_TB4588_11 - 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 > 0

11eb11e8_19ae_e84f_ad38_395c5eba4581_TB4588_11 + t - 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 > 0

Simplifying and solving for t, we get:

t > (11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 - 11eb11e8_19ae_e84f_ad38_395c5eba4581_TB4588_11)/11eb11e8_19ae_e84e_ad38_53943324ae5d_TB4588_11

t > (4/11)

So sales exceed 11eb11e8_19ae_e850_ad38_f3fc8be4c13e_TB4588_11 units at any time during the month if t > (4/11), which corresponds to April through August. Therefore, the answer is B.

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