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
[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.
Answer: 12.5 days
