f(x) = 500(1.05)x What was the average rate of change of the value of Sophia's investment from the second year to the fourth year?

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26-08-2017
Mathematics

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f(x) = 500(1.05)x What was the average rate of change of the value of Sophia's investment from the second year to the fourth year?

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jdoe0001 jdoe0001 · Answer 1 · 2017-08-26T00:36:47+02:00

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(x)=500(1.05)^x \qquad \begin{cases} x_1=2\\ x_2=4 \end{cases}\implies \cfrac{f(4)-f(2)}{4-2} \\\\\\ \cfrac{[500(1.05)^4]~-~[500(1.05)^2]}{4-2}\implies \cfrac{56.503125}{2}\implies 28.2515625[/tex]