The Function $R ( t ) = 140 + 3 t ^ { 3 }$

question 59

Multiple Choice

The function $R ( t ) = 140 + 3 t ^ { 3 }$ represents the value of the U.S. dollar in Indian rupees as a function of time t in days. Find the average rates of change of $R ( t )$ over the time intervals $[ t , t + h ]$ , where t is as indicated and $h = 1$ , $0.1$ , $0.01$ , and $0.0001$ days. Estimate (using $h = 0.0001$ ) the instantaneous rate of change of R at time $t = 7$ . Please select the correct answer rounded to the nearest whole number.

• A)443
• B) 441
• C) 437
• D) 446
• E) 444

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Definitions:

Required Rate

The minimum return that investors expect or the company specifies for an investment, project, or loan.

Investment Equipment

Assets purchased for long-term use in the production of goods or services, typically including machinery and other manufacturing tools.

Project Profitability Index

A financial metric used to evaluate the desirability of an investment or project, calculated by dividing the present value of future cash flows by the initial investment cost.

Internal Rate Of Return

The discount rate at which the net present value of an investment project is zero; the rate of return of a project over its useful life.