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)
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)
Answers
Joe
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) รท 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.
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) รท 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.