Question

a population of inseects increase 10% each day,how many days will it take to double?

Answer 1

solve
\[(1.10)^t=2\] for t

Answer 2

we can go right to the answer since
\[b^x=A\iff x=\frac{\ln(A)}{\ln(b)}\]
in your case
\[t=\frac{\ln(2)}{\ln(1.1)}\] then a calculator

Answer 3

two things you need to know for this problem
first is that to increase a number by 10% you multiply it by \(1.1\) and second is how to solve when a variable is in the exponent.
that was the second part