Graphs of Exponential Functions

Question

Suppose a population of 1100 bacteria grows by 13% each day. How many bacteria will there be in 29 days?

Answer 1

In one day the popuation grows by 13%. Let d be the number of days since there were 1100 bacteria and N(d) the number of bacteria on that day.

We are told that N(0) = 1100 and that N(d) = 1.13*N(d-1)

So N(1)=N(0)*1.13^1

N(2) = N(1)*1.13^1 = N(0)*1.13^2

N(3) = N(0)*1.13^3

If this trend continues N(29) = 1100*1.13^29

Rounding the answer you get 38,077.