For the differential equation dy/dt=ky, k is a constant, y(0)=24, and y(1)=18. What is the value of k?

The equation is separable, so solving it is trivial:

Integrating both sides gives

Given and , we find

so the answer is E.

E

Step-by-step explanation:

dy/dt = ky

1/y .dy = k .dt

ln(y) = kt + c

t = 0, y = 24

ln(24) = 0 + c

c = ln(24)

ln(y) = kt + ln(24)

t = 1, y = 18

ln(18) = k + ln(24)

k = ln(18) - ln(24)

k = ln(18/24) = ln(3/4)

d. you cannot tell because there are no values shown.