SECTEON $6\mathrm{.}2$

QUESTION $1$

Write and find the general solution of the differential equation that model the verbal statement. Evaluate the solution at the specified value of the independent variable.

$($a$)$ The rate of change of $x1$ is proportional to $x.$ When $t=0,N=250,$ and when $t=1,N=400.$ Khat is the value of $N$ when $t=4.($spoints$)$

$($b$)$ The rate of change of $y$ is proportional to $y.$ When $x=0,y=6$ and when $x=4,y=15.$ Khat is the value of $y$ when $x=8(5$pts$)$