To find the additional cost incurred when production is increased from 2 units to 13 units, we need to calculate the difference between the total cost of producing 13 units and the total cost of producing 2 units.
The total cost of producing x units is given by the antiderivative of the marginal cost function:
C(x) = ∫ C′(t) dt = 0.04t^3 - 2t^2 + 80t + C
where C is an arbitrary constant of integration.
To find the value of C, we can use the fact that the total cost of producing 2 units is known:
C(2) = 0.04(2)^3 - 2(2)^2 + 80(2) + C = 162 + C
We know from the problem statement that the total cost of producing 2 units is $162, so we can solve for C:
162 + C = C(2) = 0.12(2)^2 - 4(2) + 80 = 68
C = -94
Now we can find the total cost of producing 13 units:
C(13) = 0.04(13)^3 - 2(13)^2 + 80(13) - 94 = 1956
The additional cost incurred when production is increased from 2 units to 13 units is:
C(13) - C(2) = 1956 - 162 = $1794
Therefore, the additional cost incurred in dollars when production is increased from 2 units to 13 units is $1794.