Marginal cost. The total cost, in millions of dollars, for Marcotte Industries is given by C ( t ) = 200 − 40 e − t , where t is the time in years since the start-up date. Find each of the following. a. The marginal cost C ′ ( t ) b. C ′ ( 1 ) c. C ′ ( 5 ) (Round to the nearest thousand.) d. Find lim x → ∞ C ( t ) and lim x → ∞ C ′ ( t )
Marginal cost. The total cost, in millions of dollars, for Marcotte Industries is given by C ( t ) = 200 − 40 e − t , where t is the time in years since the start-up date. Find each of the following. a. The marginal cost C ′ ( t ) b. C ′ ( 1 ) c. C ′ ( 5 ) (Round to the nearest thousand.) d. Find lim x → ∞ C ( t ) and lim x → ∞ C ′ ( t )
A company estimates that the cost of new capacity additions follows the function f(y) =
0.0358y0.66, where y is the number of units and f(y) in millions of dollars. Demand is
increasing at a rate of 3,500 units per year. The company uses a 10% per year interest rate. What
is the present value of the cost of the next nine capacity additions?
2. An investment of $100 is placed into an account that earns interest, compounded annually, at a rate of 5% for
7 years. The amount, A, in the account can be modelled by the function A = 100(1.05)', where t is the time, in
years. What is the domain of this function?
a. (t e R, 2 7}
b. (t e R, 0 SIS7)
c. (te R, t > 7}
d. (t e R,0
6. If P(t) is the carbon emissions rate for the US, with P(t) measured in GT/year. Select the appropriate
function and units associated with the function
a. This function would tell you how much carbon
was emitted over the last decade.
O P(t)
O P'(t)
GT
O GT/year
Of P(t) dt
O GT/year²
b. This function would tell you the amount of
carbon that was emitted in 2015.
O P(t)
O P'(t)
SP(t) dt
O GT
O GT/year
O GT/year?
O GT
C.
This function would tell you how quickly carbon
emissions rate was increasing or decreasing
during the pandemic compared to pre-pandemic.
O P(t)
O P'(t)
OfP(t) dt
O GT/year
O GT/year
4
Precalculus Enhanced with Graphing Utilities (7th Edition)
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