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Andru [333]
2 years ago
10

(b) If A(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation sati

sfied by A(t).
Mathematics
1 answer:
Fantom [35]2 years ago
3 0

Answer:

A'(t) = rA(t)

Step-by-step explanation:

Given

A(t) \to Amount

Required

The differential equation

The equation for the amount is:

A(t) = A_0 * e^{rt}

Where:

A_0 \to initial amount

r \to rate

t \to time

DifferentiateA(t) = A_0 * e^{rt}

A'(t) = A_0 * r * e^{rt}

So, we have:

A'(t) = rA_0 * e^{rt}

From the question, we have: A(t) = A_0 * e^{rt}

So, the equation becomes

A'(t) = rA(t)

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3 years ago
Farmer Samantha has a cylindrical grain silo with a diameter of 12 feet and a height of 40 feet. The silo is filled with grain t
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Answer:

161,234 pounds of grain will remain in the silo

Step-by-step explanation:

In this question, we are to calculate the amount of grains that will be left in a silo if 20 cows feed on the content for 100 days.

Firstly, we need to calculate the amount of grains present in the silo.

This we can do by first calculating the volume of the silo. Since it is cylindrical in shape, we apply the formula for the volume of a cylinder.

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Now, per cubic feet, we have a weight of 48 pounds. The weight of grains thus present in the silo is thus;

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Now we need to know what will remain. We just need to subtract what is consumed by the cows from we have inside the silo

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Answer:

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Step-by-step explanation:

I'm very confused is this algebra?

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Step-by-step explanation:

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