Question

According to scientists, in t years from now in a certain country, the size
of the dog population will be given by the function f(t) = 3^5t+1, while
the size of the cat population will be given by the function g(t) = 34^t+7.
Within which time span will these populations be the same size?

Answer 1

I gave you advice with this last night. How far have you come with your working?

Answer 2

not far at all. i don't understand how to do it

Answer 3

The solution is messy, which is why im tempted to say you've typed the question wrong. Could you try using the draw button below to write f(t) and g(t) by hand so we can be sure?

Answer 4

i take it this is
\[3^{5t+1}\] and
\[34^{t+7}\]

Answer 5

in which case the first step is to write
\[3^{5t+1}=34^{t+7}\] and then
\[(5t+1)\ln(3)=(t+7)\ln(34)\] and then some algebra to solve for t