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?
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 [tex]y = 21(3^{x/7} )[/tex]
When the population is 150, then [tex]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
[/tex] A graph of y versus confirms the answer.
