Question

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

Answer 1

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.