The population of fish in a lake is changing according to the function P(t)=31t+438, where t is the number of months since the beginning of the year and P(t) is the fish population at time t. Which interpretation of the rate of change is correct?
A.
The number of fish in the lake is increasing at a constant rate of 31 fish per month.
B.
The number of fish in the lake is increasing at a constant rate of 438 fish per month.
C.
The number of fish in the lake is decreasing at a constant rate of 31 fish per month.
D.
The number of fish in the lake is decreasing at a constant rate of 438 fish per month.
The function P(t)=31t+438 is linear and follows the form P(t)=mt+b. In this form, m is the rate of change and b is the initial value. Here, the coefficient of t is 31, so the fish population changes by 31 fish per month. Because 31 is positive, the population is increasing rather than decreasing. The number 438 is the initial fish population at the start of the year, not the rate of change. Therefore, the correct interpretation is that the number of fish in the lake is increasing at a constant rate of 31 fish per month. That matches option A.
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