The average rate of change from t = 0 to t = 4 is 45. The data is better modeled by an exponential function. A possible formula to model the data is P(t) = 500 * (1.07)^t.
The average rate of change from t = 0 to t = 4 can be found by subtracting the initial population P(0) from the final population P(4) and dividing by the change in time.
In this case, the initial population is 500 and the final population is 680, so the average rate of change would be (680 - 500) / (4 - 0) = 180 / 4 = 45.
To determine whether the formula is better modeled by a linear or exponential function, we can look at the data.
Exponential growth occurs when the rate of change is proportional to the current population, while linear growth occurs when the rate of change is constant.
Since the population is increasing at a faster rate over time, the data is better modeled by an exponential function.
A possible formula to model the data is P(t) = 500 * (1.07)^t, where t represents the number of years since the initial population was introduced to the pond and 1.07 represents a growth rate of 7%.
The probable question may be:
t(years) P(t)
0 500
1 540
2 583
3 630
4 680
A population of 500 catfish was introduced to a pond. The number of catfish in the pond t years since they were first introduced can be modeled by a function P. Select values of P(t) are shown in the table. Find the average rate of change from t = 0 to t = 4. Would the formula be better modeled by a linear or exponential function? Explain. Write a formula to model the data.