Answer:
[tex]y=10e^{2t}[/tex]
Growth function
Step-by-step explanation:
We are given that
[tex]\frac{dy}{dt}=2y[/tex]
y=10 when t=0
Taking integration on both sides then we get
[tex]\int \frac{dy}{y}=\int 2dt[/tex]
[tex]lny=2dt+C[/tex]
Using formula
[tex]\int\frac{dx}{x}=lnx,\int dx=x[/tex]
[tex]y=e^{2t+C}[/tex]
[tex]y=e^C\cdot e^{2t}=Ce^{2t}[/tex]
[tex]ln x=y\implies x=e^y[/tex]
[tex]e^C=Constant=C[/tex]
Substitute y=10 and t=0
[tex]10=C[/tex]
Substitute the value of C
[tex]y=10e^{2t}[/tex]
When t tends to infinity then
[tex]\lim_{t\rightarrow \infty}=\lim_{t\rightarrow\infty}10e^{2t}=\infty[/tex]
Hence, the exponential function is growth function.
