Answer:
A -
B - Graph given below
C - Number of trouts in 5th week are 607.2
D - Population of trouts will exceed 500 on the 5th week.
Step-by-step explanation:
We are given that,
The number of trout increases by a factor of 1.5 each week and the initial population of the trout is observed to be 80.
Part A: So, the explicit formula representing the situation is,
, where f(t) represents the population of trouts after 't' weeks.
Part B: The graph of the function can be seen below.
It can be seen that the function is an exponential function.
Part C: It is required to find the number of trouts in the 5th week.
So, we have,
i.e.
i.e. f(5) = 607.2
Thus, the number of trouts in 5th week are 607.2
Part D: We are given that the trout population exceeds 500.
It is required to find the week in which this happens.
So, we have,
i.e.
i.e.
i.e.
i.e.
i.e.
i.e. t > 4.5
As, t represents the number of weeks. So, to nearest whole, t = 5.
Thus, the population of trouts will exceed 500 on the 5th week.
