Answered: A certain investment is subject to…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 2TI: Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time...

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Question

A certain investment is subject to continuous compounding. The value of the investment after t years is given by

V = 4000e^0.04t

dollars.

(a)

Make a graph of the value of the investment over the first 20 years.

(b)

Is the graph concave up or concave down?

concave upconcave down

Explain in practical terms what the concavity means.

The value of the investment is increasing at an increasing rate, so it grows more rapidly in later years than in earlier years.The value of the investment is increasing at a constant rate, so it grows at the same rate in later years as it does in earlier years. The value of the investment is decreasing at an increasing rate, so it shrinks more rapidly in later years than in earlier years.The value of the investment is increasing at a decreasing rate, so it grows less rapidly in later years than in earlier years.The value of the investment is decreasing at a decreasing rate, so it shrinks less rapidly in later years than in earlier years.

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