Question

Alma is studying a population of frogs for an experiment. At the beginning of her experiment, there are 14 frogs. The population doubles every 12 days. What function can Alma use to model the number of frogs?

a) N(t) = 14(2^(t/12))
b) N(t) = 14(2t)
c) N(t) = 14(2^(12t))
d) N(t) = 14(2t/12)

Answer 1

Alma can model the frog population using the exponential function N(t) = 14(2^(t/12)), which reflects the population doubling every 12 days starting with an initial count of 14 frogs.

Step-by-step explanation:

The function that Alma can use to model the number of frogs, where the population doubles every 12 days, is N(t) = 14(2^(t/12)). This exponential function correctly represents the growth of the frog population over time, t, in days.

Exponential growth is characterized by a constant doubling period, which in this case is every 12 days.

Since the initial population is 14 frogs, the base number of frogs is 14. We use the exponent t/12 because the population doubles every 12 days, which means that for each additional 12-day period, we multiply the population by 2.

To model the number of frogs in this experiment, Alma can use the function N(t) = 14(2^(t/12)). This function represents exponential growth, where the number of frogs doubles every 12 days. The initial population of 14 is multiplied by 2 raised to the power of t/12, where t represents the number of days elapsed.