Question

The original value of a car is $22,000 and it depreciates (loses value) by 15% each year. What is the value of the car after three years?

A: $74.25
B: $15,895
C: $56,595
D: $13,510.75

A ball dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. How far will the ball have traveled when it hits the ground for the fifth time?

A: 34.5 feet
B: 1.5 feet
C: 12 feet
D: 24 feet

Which of the following are geometric sequences?
Check all that apply

10, 5, 2.5, 1.25, 0.625, 0.3125

5, 10, 15, 20, 25

1, 1, 2, 3, 8, 13,

-9, -3, -1, -1/3, -1/9, -1/27

Answer 1

Answer on Question #56676 – Math – Calculus

1. The original value of a car is $22,000 and it depreciates (loses value) by 15% each year. What is the value of the car after three years?

A: $74.25

B: $15,895

C: $56,595

D: $13,510.75

Solution

Annual depreciation is 15%, thus the remaining price is 85% of previous value.

Value after $n$ years: $P_n = P_0 \times 0.85^n$

Value after 3 years: $P_3 = \$22,000 \times 0.85^3 = \$13,510.75$

Answer: D: $13,510.75

2. A ball dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. How far will the ball have traveled when it hits the ground for the fifth time?

A: 34.5 feet

B: 1.5 feet

C: 12 feet

D: 24 feet

Solution

The height which the ball reaches after $n$ hits: $H_n = H_0 \times 0.5^n$

The height after $1^{\text{st}}$ hit: $H_1 = 12 \times 0.5^1 = 6$ ft

The height after $2^{\text{nd}}$ hit: $H_2 = 12 \times 0.5^2 = 3$ ft

The height after $3^{\text{rd}}$ hit: $H_3 = 12 \times 0.5^3 = 1.5$ ft

The height after $4^{\text{th}}$ hit: $H_4 = 12 \times 0.5^4 = 0.75$ ft

The total distance traveled by ball:

$D = H_0 + 2H_1 + 2H_2 + 2H_3 + 2H_4 = 34.5$ ft

Answer: A: 34.5 feet

3. Which of the following are geometric sequences?

Check all that apply

10, 5, 2.5, 1.25, 0.625, 0.3125 +

5, 10, 15, 20, 25

1, 1, 2, 3, 8, 13,

-9, -3, -1, -1/3, -1/9, -1/27 +

Correct options marked with “+”. Reason: the ratio $r$ is the same for each pair of terms of the sequence.

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