Question

Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.

Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)

Part B: Write the equation obtained in Part A using function notation.(2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Answer 1

PART A:
1. The curve of cost vs time is concave down.
2. This suggests a power curve of the form: a(time)^n = rent, where a and n are to be determined.
3. Write: at^n = r
4. Take nstural logarthm of both sides: ln(a) ÷ n[ln(t)] = ln(r)
5. Use given data:
r = 225 when t = 2 and
r = 480 when t = 5
6. Write resulting equations and solve:
ln(a) + 0.69t = 5.42
ln(a) + 1.62t = 6.17
Therefore a = 127.71 and n=0.82
7. The final result is:
127.71(t^0.82) = r
PART B:
r(t) = 127.71(t^0.82)
PART C:
The x-axis is time in days, the y axis is rent in hundreds of dollars.