Homework SourseFill in the missing values in the table given if you know th
Fill in the missing values in the table given if you know that dy/dt=0.2y. Assume the rate of growth given by dy/dt is approximately constant over each unit time interval and that the initial value of y is 6.
Table:
t-0-1-2-3-4
y-6-?-?-?-?
(fill in the missing values where there is a question mark)
I got:
t = 1, y = 7.33
At t = 2 , y = 8.95
At t = 3 , y =10.93
At t = 4 , y = 13.35
but it is wrong, Help?
Table:
t-0-1-2-3-4
y-6-?-?-?-?
(fill in the missing values where there is a question mark)
I got:
t = 1, y = 7.33
At t = 2 , y = 8.95
At t = 3 , y =10.93
At t = 4 , y = 13.35
but it is wrong, Help?
Solution
sol dy/dt = 0.2y dy/y = 0.2 dt lny = 0.2t + lnC lny - lnC = 0.2t ln(y/C) = 0.2t y = Ce^(0.2t) `````````````````` when t = 0, y = 7 y = Ce^(0.2t) 7 = Ce^(0.2 x 0) e^0 = 1 so C = 7 y = 7e^(0.2t) ```````````````` y(0) = 7 y(1) = 8.5498 y(2) = 10.4428 y(3) = 12.7548 y(4) = 15.5788
