A new species of fish is released into a lake and the fish multiply quickly, the growth of their population is modeled by the exponential function: P(t) = 7b^t , where t is the time in weeks after the reales and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function: P(t) = 7(2)^t is used to model the growth. interpret the significance of 2 in the function as it applies to the situation.

Question

A new species of fish is released into a lake and the fish multiply quickly, the growth of their population is modeled by the exponential function: P(t) = 7b^t , where t is the time in weeks after the reales and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function: P(t) = 7(2)^t is used to model the growth. interpret the significance of 2 in the function as it applies to the situation.

a) The population is doubling each week.
b) the population is counted every 2 weeks.
c) the population is increasing by 2 fish each week
d) the population is doubling each month

Answer 1

a) The population is doubling each week.

In the function P(t) = 7(2)^t, the base value, 2, represents the rate at which the population is increasing. As the exponent t increases by 1 for each week, the value of (2)^t doubles each time. This means that with each passing week, the population is doubling in size. Therefore, the significance of 2 in the function is that the population is doubling each week.