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aliina [53]
2 years ago
7

Harold wants to borrow $1,000 for 3 years. The interest rate is 6%. How much interest will he pay over the course of the loan?

Mathematics
1 answer:
kotykmax [81]2 years ago
7 0

Answer:

that is the solution to the question

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The population P(t) of a species satisfies the logistic differential equation dP/dt= P(2-(P/5000)) where the initial population
Elis [28]
A logistic differential equation can be written as follows:
\frac{dP}{dt} = rP[1- \frac{P}{K}]

where r = growth parameter and K = carrying parameter.

In order to write you equation in this form, you have to regroup 2:
\frac{dP}{dt} = 2P[1- \frac{P}{10000}]

Therefore, in you case r = 2 and K = 10000

To solve the logistic differential equation you need to solve:

\int { \frac{1}{[P(1- \frac{P}{K})] } } \, dP =  \int {r} \, dt

The soution will be:

P(t) = \frac{P(0)K}{P(0)+(K-P(0)) e^{-rt} }

where P(0) is the initial population.

In your case, you'll have:

P(t) = <span>\frac{3E7}{3E3+7E3 e^{-2t} }

Now you have to calculate the limit of P(t).
We know that
</span>\lim_{t \to \infty}  e^{-2t} -\ \textgreater \  0  &#10;

hence,

\lim_{t \to \infty} P(t) =  \lim_{t \to \infty}  \frac{3E7}{3E3+0} =  10^{4}<span>

</span><span>

</span>
5 0
2 years ago
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