A certain quantity grows exponentially over time. The initial quantity at t = 0 is 1,000. The quantity grows by a factor of 3%. What is the quantity at t = 5 to the nearest whole number?

Question

michele_laino · Answer

If I write $$Q(t)=Q _{0}\times e ^{t}$$ where Q(t) is the quantity at generic time t, $$Q _{0}$$ is the same quantity at initial time t=0, and $$e=2.71828...$$we have $$Q _{0}=1,000$$
from the text of your problem, furthermore, whenQ is grew, at the time $$t ^{*}$$, we can write:
$$Q(t ^{*})=Q _{0}\times e ^{t ^{*}}$$, please find the ratio $$Q(t ^{*})/Q _{0}$$