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omeli [17]
3 years ago
11

Determining Exponential Growth and Decay in Exercise, use the given information to write an exponential equation for y. Does the

function represent exponential growth or exponential decay?
dy/dt = 2y, y = 10 when t = 0
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
4 0

Answer:

y=10e^{2t}

Growth function

Step-by-step explanation:

We are given that

\frac{dy}{dt}=2y

y=10 when t=0

Taking integration on both sides then we get

\int \frac{dy}{y}=\int 2dt

lny=2dt+C

Using formula

\int\frac{dx}{x}=lnx,\int dx=x

y=e^{2t+C}

y=e^C\cdot e^{2t}=Ce^{2t}

ln x=y\implies x=e^y

e^C=Constant=C

Substitute y=10 and t=0

10=C

Substitute the value of C

y=10e^{2t}

When t tends to infinity then

\lim_{t\rightarrow \infty}=\lim_{t\rightarrow\infty}10e^{2t}=\infty

Hence, the exponential function is growth function.

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3 years ago
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Answer:

As Given, x+y=w+z

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3 years ago
n an amusement park, the bumper cars are sometimes becoming disabled and in need of repair. The repairman can fix the disabled b
grigory [225]

Answer:

1 hour 20 minutes

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Answer:

39

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