Question

The number of purchases made on a new online store is modeled by
p(d) 15d + 45, where d is the number of days since the store opened.
The average amount spent in dollars per purchase is modeled by
s(d) = 0.15d? – 4d + 80. Write a function R(d) to model the total daily
revenue. Then predict the total amount of revenue on the 23rd day.
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Answer 1

The total amount of revenue on the 23rd day is 322.65

Given the following parameters:

• purchases made p(d) = 15d + 45
• sales made  s(d) = 0.15d² – 4d + 80

The revenue will be exprssed as:

r(d) = s(d) - p(d)

r(d) = 0.15d² – 4d + 80 - (15d + 45)

r(d) = 0.15d² – 19d + 35

Hence a function R(d) to model the total daily  revenue is r(d) = 0.15d² – 19d + 35

To get the total amount of revenue on the 23rd day, you will substitute t = 23 into the function

r(d) = 0.15d² – 19d + 35

r(23) =  0.15(23)² – 19(23) + 35

r(23) = 79.35 - 437 + 35

r(23) = -322.65

Hence the total amount of revenue on the 23rd day is 322.65

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