Question

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?

Answer 1

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 \[Q(t ^{*})/Q _{0}\]