Answer: (B) 3 times as fast
Step-by-step explanation:
rate of change is the "slope" between the given interval.
f(x) = 125(.9)ˣ
f(1) = 125(.9)¹
= 112.5
f(5) = 125(.9)⁵
= 73.8
[tex]\dfrac{f(5) - f(1)}{5 - 1} = \dfrac{73.8-112.5}{5-1} = -\dfrac{38.7}{4} = -9.675[/tex]
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f(11) = 125(.9)¹¹
= 39.2
f(15) = 125(.9)¹⁵
= 25.7
[tex]\dfrac{f(15) - f(11)}{15 - 11} = \dfrac{39.2-25.7}{15-11} = -\dfrac{13.5}{4} = -3.375[/tex]
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The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.
