Interpreting exponential parameters. Game on.

Interpreting exponential parameters is a grade 9 math skill aligned to Common Core standard HSF.LE.B.5. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 interpreting exponential parameters problems our math games drill.

CCSS HSF.LE.B.510 questions in the bank
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Warm-upeasy

The function gg is defined by g(n)=80(1.12)ng(n) = 80(1.12)^{n}. The function models the price, in dollars, of a limited-edition poster nn years after it was first sold. Which statement is the best interpretation of the growth factor 1.121.12 in this context?

The growth factor is 1.121.12. Each time nn increases by 11, the price is multiplied by 1.121.12. That means each year the price is 112%112\% of the previous year's price, a 12%12\% increase.

Mid-gameeasy

The function pp is defined by p(w)=1,250(1.04)wp(w) = 1{,}250(1.04)^{w}. The function models a savings balance, in dollars, ww weeks after an account is opened. Which statement is the best interpretation of 1,2501{,}250 in this context?

When w=0w = 0, p(0)=1,250p(0) = 1{,}250. So $1,250\text{\char36}1{,}250 is the balance when the account is opened.

Mid-gameeasy

The function rr is defined by r(t)=60(1.09)tr(t) = 60(1.09)^{t}. The function models the number of registered runners in a charity race tt years after the first race. Which statement is the best interpretation of the growth factor 1.091.09 in this context?

The growth factor is 1.091.09. Each time tt increases by 11, the number of runners is multiplied by 1.091.09. That means each year the number of runners is 109%109\% of the previous year's number, a 9%9\% increase.

Mid-gameeasy

The function mm is defined by m(d)=500(0.92)dm(d) = 500(0.92)^{d}. The function models the mass, in grams, of a sample dd days after a reaction begins. Which statement is the best interpretation of the decay factor 0.920.92 in this context?

The decay factor is 0.920.92. Each time dd increases by 11, the mass is multiplied by 0.920.92. That means each day 92%92\% of the previous day's mass remains, so the mass decreases by 8%8\% of the previous day's amount.

Mid-gameeasy

The function vv is defined by v(y)=18,000(0.88)yv(y) = 18{,}000(0.88)^{y}. The function models the value, in dollars, of a used scooter yy years after it is purchased. Which statement is the best interpretation of 18,00018{,}000 in this context?

When y=0y = 0, v(0)=18,000v(0) = 18{,}000. So $18,000\text{\char36}18{,}000 is the value of the scooter when it is purchased.

Mid-gameeasy

The function cc is defined by c(x)=40(1.25)xc(x) = 40(1.25)^{x}. The function models the number of colonies of bacteria xx hours after a culture is started. Which statement is the best interpretation of the growth factor 1.251.25 in this context?

The growth factor is 1.251.25. Each time xx increases by 11, the number of colonies is multiplied by 1.251.25. That means each hour the number of colonies is 125%125\% of the previous hour's number, a 25%25\% increase.

Mid-gameeasy

The function ss is defined by s(t)=90(0.60)ts(t) = 90(0.60)^{t}. The function models the number of songs still on a playlist tt weeks after a cleanup begins. Which statement is the best interpretation of the decay factor 0.600.60 in this context?

The decay factor is 0.600.60. Each time tt increases by 11, the number of songs is multiplied by 0.600.60. That means each week 60%60\% of the previous week's songs remain.

Buzzer beatereasy

The function bb is defined by b(k)=15(1.06)kb(k) = 15(1.06)^{k}. The function models the number of birdhouses in a park kk years after a volunteer project begins. Which statement is the best interpretation of 1515 in this context?

When k=0k = 0, b(0)=15b(0) = 15. So 1515 is the number of birdhouses when the volunteer project begins.

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