# Chapter 7 - Exponents and Exponential Functions - 7-7 Exponential Growth and Decay - Practice and Problem-Solving Exercises - Page 460: 40

It depends on the length of time. If the account is to be held for more than 16.938 years, then the account earning 6% would accrue more interest. If the account is to be held for less than 16.938 years, then the account earning 5% would accrue more interest.

#### Work Step by Step

$500*(1+(.06/4))^{4*x}$ $600*(1+.05)^x$ $500*(1+(.06/4))^{4*x}$ =$600*(1+.05)^x$ $500*(1+(.06/4))^{4*x}/500$ =$600*(1+.05)^x/500$ $(1+(.06/4))^{4*x} =1.2*(1+.05)^x$ $1.015^{4*x} =1.2*(1.05)^x$ $1.015^{4*x}/(1.05)^x =1.2*(1.05)^x/(1.05)^x$ $1.015^{4*x}/(1.05)^x = 1.2$ (A calculator was used to determine the value of x.) $x=16.938$

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