Exponential Growth and Decay

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Exercises 9 Let's start by recalling the general formula of exponential growth and exponential decay. Exponential growth​y=a(1+r)t​Exponential decay​y=a(1−r)t​ In both cases, a>0 is the initial amount and r>0 is the rate of growth/decay written in decimal form. Moreover, for exponential decay, r is less than 1. Let's rewrite the given function to match any of the above formats. f(t)=1500(1.074)tWrite as a sumf(t)=1500(1+0.074)t Our function represents an exponential growth with initial amount a = 1500 and rate of growth r = 0.074. To rewrite the rate of growth as a percent, we move the decimal point 2 places to the right. r=0.074⇔r=7.4%​ Finally, to evaluate the function when t=5, we will substitute 5 for t in the given formula and simplify. f(t)=1500(1.074)tt=5f(5)=1500(1.074)5 Simplify right-hand side and Calculate powerf(5)=1500(1.428964392)Multiplyf(5)=2143.446588 f(5)≈2143.4
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Exercises 34 Let's pay close attention to how the x-variable increases and to the behavior of the y-variable.We see that, as x increases by 1, y is multiplied by different numbers. So, the table represents neither an exponential growth function nor an exponential decay function.
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