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3 years ago

7.

Mathematics

2 answers:

Vadim26 [7]3 years ago

8 0

Answer:

2,160

Step-by-step explanation

x=12

18,000=100

x= 2,160

Zarrin [17]3 years ago

5 0

B. $2,160.00

18,000.00 • .12

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Step-by-step explanation:

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3 years ago

Find the solution to dy/dt = 7 y satisfying y(9) = 5

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$\rm \dfrac{dy}{dt}=7y,\qquad\qquad\qquad y(9)=5$

I'm not sure what methods you've learned up to this point but one option is to apply separation of variables:

$\rm \dfrac{dy}{y}=7dt$

and then integrate from there,

$\rm ln|y|=7t+c$

exponentiate to isolate y,

$\rm |y|=e^{7t+c}$

Apply exponent rule,

$\rm |y|=e^c e^{7t}$

rename this e^c as some new constant, perhaps A,

$\rm \pm y=A e^{7t}\qquad\qquad A>0$

This A can only be positive, non-zero, but absorbing the plus/minus fixes that restriction,

$\rm y=A e^{7t}\qquad\qquad A\ne0$

Use your initial information to solve for this unknown value A,

$\rm y(9)=A e^{7\cdot9}=5$

solving for A, dividing by the exponential,

$\rm A=5e^{-63}$

So we get a final result of

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apply exponent rule again to get a better looking answer, and factor,

$\rm y(t)=5e^{7(t-9)}$

Lemme know if too confusing.

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3 years ago