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)

180 square centimeters

step-by-step explanation:

step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00