The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K23.Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) = 2t4 + 3t + 149/t + 2(a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
The number of units Q of a particular commodity that will be produced with K
thousand dollars of capital expenditure is modeled by Q(K) = 500 K
2
3.
Suppose that capital expenditure varies with time in such a way that t months from now
there will be K(t) thousand dollars of capital expenditure, where
K(t) = 2t4 + 3t + 149/t + 2
(a) What will be the capital expenditure 3 months from now? How many units will be produced
at this time?
(b) At what rate will production be changing with respect to time 5 months from now?
Will production be increasing or decreasing at this time?
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