Question

There are currently 21 frogs in a (large) pond. The frog population grows exponentially, tripling every 7 days. How long will it take (in days) for there to be 150 frogs in the pond?

Answer 1

Let x =  number of days

The initial number of frogs  = 21.
The number of frogs triples every 7 days.
The exponential function that models the number of frogs with respect to the number of days is
$y = 21(3^{x/7} )$

When the population is 150, then
$21(3^{x/7}) = 150 \\\\ 3^{x/7} = 150/21 \\\\ \frac{x}{7} ln(3) = ln(150/7) \\\\ x = 7( \frac{ln(150/21)}{ln(3)} ) = 12.527$
A graph of y versus confirms the answer.

Answer:  12.5 days