Question

Write and solve the differential equation that models the verbal statement.
The rate of change of N is proportional to N. (Use k for the proportionality constant.)
dN
dt
=

N(t) =

I mainly need help with the bottom part below this sentence.
Evaluate the solution at the specified value of the independent variable.
When t = 0, N = 250, and when t = 1, N = 300. What is the value of N when t = 4?
N(4) =

Answer 1

so, you have
dN/dt = kN
dN/N = k dt
log N = kt + log c
N = c*e^(kt)
Now plug in the points (0,250) and (1,300) to find c and k
250 = c*1, so c=250
N = 250e^(kt)
similarly to find k.
Then use the result to find N(4)

Answer 2

To me that don’t make sense