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Suppose V(t) is an exponential function growing at a continuous percent growth rate. Then V can be expressed as a function of time t (in years) in two ways. • V(t) = Aekt, where A is the initial investment and k is the continuous percent growth rate. • V(t) = A(B¹), where A is the initial investment and B is the growth factor. a. If r is the effective annual interest rate of the investment (expressed as a decimal), explain why B = 1 + r. b. Explain why B = ek.

Suppose V(t) is an exponential function growing at a continuous percent growth rate. Then V can be expressed as a function of time t (in years) in two ways. • V(t) = Aekt, where A is the initial investment and k is the continuous percent growth rate. • V(t) = A(B¹), where A is the initial investment and B is the growth factor. a. If r is the effective annual interest rate of the investment (expressed as a decimal), explain why B = 1 + r. b. Explain why B = ek.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8 Suppose V(t) is an exponential function growing at a continuous percent growth rate. Then V can be expressed as a function of time t (in years) in two ways. V V(t) = Aet, where A is the initial investment and k is the continuous percent growth rate. V(t) = A(B¹), where A is the initial investment and B is the growth factor. a. If r is the effective annual interest rate of the investment (expressed as a decimal), explain why B = 1 + r. b. Explain why B = ek. ●
Transcribed Image Text:8 Suppose V(t) is an exponential function growing at a continuous percent growth rate. Then V can be expressed as a function of time t (in years) in two ways. V V(t) = Aet, where A is the initial investment and k is the continuous percent growth rate. V(t) = A(B¹), where A is the initial investment and B is the growth factor. a. If r is the effective annual interest rate of the investment (expressed as a decimal), explain why B = 1 + r. b. Explain why B = ek. ●
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