The equation is [tex]p = 5e^{t} +20[/tex].
Integration
It is a method of summing up parts to find the whole. It is a reverse process of differentiation.
Given
dp/dt=5e^t
To find
The value of p.
How to get the value of p?
dp/dt=5e^t is given
[tex]\begin{aligned} \dfrac{dp}{dt} &= e^{t} \\\int dp &= \int {5e^{t} } \, dt \\\int dp &= 5 \int {e^{t} } \, dt \\p &= 5e^{t} +c\\\end{aligned}[/tex]
It is given that at t=0, p will be 25, then
[tex]p = 5e^{t} + c\\c = p - 5e^{t}\\c= 25 - 5e^{0}\\c= 25 - 5 * 1\\c= 20[/tex]
Hence the equation will be [tex]p = 5e^{t} +20[/tex].
Thus, the equation is [tex]p = 5e^{t} +20[/tex].
More about the integration link is given below.
https://brainly.com/question/18651211
