It is estimated that t weeks from now, the number of commuters using a new subway line will be increasing at the rate of 18t^2 + 500 per week. Currently, 8, 000 commuters use the subway. How many will be using it 5 weeks from now?
Hi! I really do not get how to solve this with integration.
the number increases at the rate of 18t^2 + 500 per week
dn/dt = 18t^2 + 500
n = 6t^3 + 500t + c
n(0) = 8000, so c = 8000
Now find n(5)