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3 years ago

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You inherit $5,000 from your Uncle Harold. The bad news is that the money must sit in a bank account for the next 10 years until

you can use it. The account earns 7.2% interest, compounded annually. This means that you will need to multiply the amount of money by 1.072 to determine how much money remains at the end of the next year.
HELPPP PLEASEE

1 answer:

Eduardwww [97]3 years ago

6 0

Answer:

what the world is this question its so long and hard

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Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsda

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The doomsday is 146 days

<em></em>

Step-by-step explanation:

Given

$\frac{dy}{dt} = ky^{1 +c}$

First, we calculate the solution that satisfies the initial solution

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$\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}$

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$-\frac{y_0^{-c}}{c} = k*0+C$

$-\frac{y_0^{-c}}{c} = C$

$C =-\frac{y_0^{-c}}{c}$

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$-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}$

Multiply through by -c

$y^{-c} = -ckt+y_0^{-c}$

Take exponents of $-c^{-1$

$y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}$

$y = [-ckt+y_0^{-c}]^{-c^{-1}$

$y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}$

i.e.

$y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}$

Next:

$t= 3$ i.e. 3 months

$y_0 = 2$ --- initial number of breeds

So, we have:

$y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}$

-----------------------------------------------------------------------------

We have the growth term to be: $ky^{1.01}$

This implies that:

$ky^{1.01} = ky^{1+c}$

By comparison:

$1.01 = 1 + c$

$c = 1.01 - 1 = 0.01$

$y(3) = 16$ --- 16 rabbits after 3 months:

-----------------------------------------------------------------------------

$y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}$

$16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}$

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$16 = [-0.03 k + 0.9931]^{-100}$

Take -1/100th root of both sides

$16^{-1/100} = -0.03k + 0.9931$

$0.9727 = -0.03k + 0.9931$

$0.03k= - 0.9727 + 0.9931$

$0.03k= 0.0204$

$k= \frac{0.0204}{0.03}$

$k= 0.68$

Recall that:

$-\frac{y^{-c}}{c} = kt+C$

This implies that:

$\frac{y_0^{-c}}{c} = kT$

Make T the subject

$T = \frac{y_0^{-c}}{kc}$

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$T = \frac{2^{-0.01}}{0.68 * 0.01}$

$T = \frac{2^{-0.01}}{0.0068}$

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$T = 146.04$

<em>The doomsday is 146 days</em>

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