Question

Air pressure may be represented as a function of height above the surface of earth as shown below.
p(h) = Poe^ -.00012h

1: In this function, P0 is air pressure at sea level, and h is measured in meters. Which of the following equations will find the height at which air pressure is 75% of the air pressure at sea level?

A: 0.75Po=Poe^-0.00012h
B: Po=0.75Poe^-0.00012h
C: h=0.75e^-0.00012
D: 0.75=h ∙ e^-0.00012

2: If you put $ 2,000 in a savings account that pays 6% interest compounded continuously, how much money will you have in your account in 4 years? Assume you make no additional deposits or withdraws.

A: $2,983.65
B: $2,542.50
C: $8,326.49
D: $3,168.15

Answer 1

Answer on Question #56716 – Math – Calculus

Question

1. Air pressure may be represented as a function of height above the surface of earth as shown below:

$$p(h) = p_0 e^{-0.00012h}.$$

In this function, $p_0$ is air pressure at sea level and $h$ is measured in meters. Which of the following equations will find the height at which air pressure is 75% of the air pressure at sea level?

A: $0.75p_0 = p_0 e^{-0.00012h}$

B: $p_0 = 0.75p_0 e^{-0.00012h}$

C: $h = 0.75 e^{-0.00012}$

D: $0.75 = h e^{-0.00012}$

Answer: A: $0.75p_0 = p_0 e^{-0.00012h}$

Question

2. If you put $2,000 in a savings account that pays 6% interest compounded continuously, how much money will you have in your account in 4 years? Assume you make no additional deposits or withdraws.

A: $2,983.65

B: $2,542.50

C: $8,326.49

D: $3,168.15

Solution

Using continuous compounding we have

$$Sum = \$2000 \cdot e^{0.06 \cdot 4} = \$2,542.50$$

Answer: B: $2,542.50.

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