I need help with a calc II homework problem, if anyone could help I'd really appreciate it!
The rate of growth of a tumor is proportional to the size of a tumor.
(a) Write a differential equation satisfied by S, the size of the tumor, in mm, as a function of time t. Assume the proportionality constant, k, is positive.
(I got this part right)
dS/dt=kS
(b) Solve the differential equation if the tumor is 7 mm at time t =0, but grows to 14 mm by time t = 4.
(this is the part I need help with)
S(t) = ?
I thought the answer was 7*e^((ln(7)/4)*t) but I was wrong and I don't know where I made the mistake.
The rate of growth of a tumor is proportional to the size of a tumor.
(a) Write a differential equation satisfied by S, the size of the tumor, in mm, as a function of time t. Assume the proportionality constant, k, is positive.
(I got this part right)
dS/dt=kS
(b) Solve the differential equation if the tumor is 7 mm at time t =0, but grows to 14 mm by time t = 4.
(this is the part I need help with)
S(t) = ?
I thought the answer was 7*e^((ln(7)/4)*t) but I was wrong and I don't know where I made the mistake.
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Where did the " ln 7 " arise ??..14 = 7 e^(k4)---> 2 = e^(...)