SAT Math · Nonlinear functions · easy

A bacteria population is modeled by N(t) = 500(1.12)^t, where t is measured in hours. By what percent does the population grow each hour?

A bacteria population is modeled by N(t)=500(1.12)tN(t) = 500(1.12)^t, where tt is measured in hours. By what percent does the population grow each hour?

Answer and explanation

Answer: 12

In an exponential model N(t)=N0btN(t) = N_0 b^t, the base bb is the growth factor per time period. Here b=1.12=1+0.12b = 1.12 = 1 + 0.12, so each hour the population is multiplied by 1.12, an increase of 12%. The answer is 12. Common wrong answers are 112, the percent of the previous value after one hour rather than the increase, and 500, the initial population. Another is 1.12, which misreads the decimal as a percent. Subtract 1 from the base and convert the decimal to a percent: 0.12=12%0.12 = 12\%.

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