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Luda [366]
3 years ago
9

Ms. Chambers applied for a home improvement loan that has an annual interest rate of 6%, compounded monthly. The following expre

ssion represents the total amount that she will spend to pay off the loan in t years.
What is the exponential expression in the form (b)c that reveals the monthly interest rate on the loan?

Mathematics
1 answer:
patriot [66]3 years ago
3 0

Answer:

B. 120,000(1.005)^{12t}

Step-by-step explanation:

We are given that,

The expression representing the amount of the loan with 6% interest rate is,

Loan amount = 120,000(1.06)^t = 120,000(1+0.06)^t

Now, we want to find the amount which represents the loan being compounded monthly.

Thus, we have that,

Loan amount compounded monthly = 120,000(1+\frac{0.06}{12})^{12t}

i.e. Loan amount compounded monthly = 120,000(1+0.005)^{12t}

i.e. Loan amount compounded monthly = 120,000(1.005)^{12t}

Hence, the expression representing the monthly interest rate on the loan is 120,000(1.005)^{12t}.

So, option B is correct.

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PLEASE SHOW WORK
CaHeK987 [17]

(C)

Step-by-step explanation:

The volume of the conical pile is given by

V = \dfrac{\pi}{3}r^2h

Taking the derivative of V with respect to time, we get

\dfrac{dV}{dt} = \dfrac{\pi}{3}\dfrac{d}{dt}(r^2h)

\:\:\:\:\:\:\:= \dfrac{\pi}{3}\left(2rh\dfrac{dr}{dt} + r^2\dfrac{dh}{dt}\right)

Since r is always equal to h, we can set

\dfrac{dr}{dt} = \dfrac{dh}{dt}

so that our expression for dV/dt becomes

\dfrac{dV}{dt} = \dfrac{\pi}{3}\left(3r^2\dfrac{dh}{dt}\right)

\:\:\:\:\:\:\:= \pi r^2\dfrac{dh}{dt}

Solving for dh/dt, we get

\dfrac{dh}{dt} = \dfrac{1}{\pi r^2}\dfrac{dV}{dt}

\:\:\:\:\:\:\:= \dfrac{1}{9\pi\:\text{m}^2}(36\:\text{m}^3\text{/s})

\:\:\:\:\:\:\:= \dfrac{4}{\pi}\:\text{m/s}

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3 years ago
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3 years ago
An atom of the element zinc has an atomic number of 30 and a mass number of 65. How many protons does an uncharged zinc atom hav
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4 years ago
The period of a pendulum is the time the pendulum takes to swing back and forth one full time. The function I = 0.81t^2 relates
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Answer:

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