Answer:
the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion
Step-by-step explanation:
From the given information:
Let consider y to represent the number of years after 1999
Then the population in time (y) can be expressed as:
P(y) = 9400y + 924900
The average annual income can be written as:
A(y) = 1400y + 30388
The total personal income = P(y) × A(y)
The rate at which the total personal income is rising is T'(y) :
T'(y) = P'(y) × A(y) + P(y) × A'(y)
T'(y) = (9400y + 924900)' (1400y + 30388) + (9400y + 924900) (1400y + 30388)'
T'(y) = 9400(1400y + 30388) + (9400y + 924900) 1400
Since in 1999 y =0
Then:
T'(0) = 9400(1400(0) + 30388) + (9400(0) + 924900) 1400
T'(0) = 9400(30388) + (924900)1400
T'(0) = $1,580,507,200 billion
Therefore; the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion
