Question

Solve the following example: The total cost of ‘t’ toy cars is given by C=5(2^t)+17. Find the marginal cost and average cost at t = 3.

Answer 1

Total cost of ‘t’ toy cars, C = 5(2^t) + 17

Marginal Cost =`("dC")/"dt"`

= `d/dt [5(2^t) + 17]`

=`5"d"/"dt"(2^"t")+"d"/"dt"(17)`

= 5(2^t . log 2) + 0
= 5(2^t . log 2)
When t = 3,
Marginal cost =` (("dC")/("dt"))_("t" = 3)`

= 5(2³. log 2)
= 40 log 2
Average cost =`"C"/"t"= (5(2)^"t"+17)/t`

When t = 3, averagecos = `(5(2^3) + 17)/3`

= `(40+ 17)/3` = 19

∴ at t = 3, Marginal cost is 40 log 2 and Average cost is 19.