Answer:
[tex]y=30e^{-4t}[/tex]
Exponential decay.
Step-by-step explanation:
We are given that
[tex]\frac{dy}{dt}=-4y[/tex]
y=30 when t=0
Taking integration on both sides then we get
[tex]\int \frac{dy}{y}=-4\int dt[/tex]
[tex]lny=-4t+C[/tex]
By using the formula [tex]\int \frac{dx}{x}=ln x,\int dx=x[/tex]
[tex]y=e^{-4t+C}[/tex]
[tex]y=e^{C}e^{-4t}=Ce^{-4t}[/tex]
Where[tex]e^C=Constant=C[/tex]
[tex]y=Ce^{-4t}[/tex]
Substitute y=30 and t=0
[tex]30=C[/tex]
[tex]y=30e^{-4t}[/tex]
Apply limit t tends to infinity
[tex]\lim_{t\rightarrow \infty}=\lim_{t\rightarrow\infty}30e^{-4t}=0[/tex]
The value of function decreases with time therefore, it is an exponential decay.
