Briggs and Cochran page 377
A cultore of cells in a lab has a population of 100 cells when nutrients are added at time t=0. Suppose population N(t) increases at a rate given by
Find N(t) for t≥0
N'(t)=90e^-0.1t cells per hour.
N(t)=N(0) + t⌠0 N'(x)dx
100 + t⌠0 90e^-0.1x dx
100 + [(90/-0.1)e^-0.1x]t|0
Now I get confused as to how the next step is 1000. Also, I thought when you integrate an exponential function, you do x^n+1 divided by n+1. But 1 is not added to -0.1 either on the exponent of e or on the -.01 in the denominator. Here’s what the book came up with: