Simone is an ecologist who studies the change in the tiger population of Siberia over time. The relationship between the elapsed time t, in years, since Simone started studying the population, and the number of tigers, N_("year ")(t), is modeled by the following function: N_("year ")(t)=612*((2)/(3))^(t) Complete the following sentence about the monthly rate of change in the tiger population. Round your answer to two decimal places. Every month, the number of tigers decays by a factor of

Question

Simone is an ecologist who studies the change in the tiger population of Siberia over time. The relationship between the elapsed time  t, in years, since Simone started studying the population, and the number of tigers,  N_("year ")(t), is modeled by the following function:  N_("year ")(t)=612*((2)/(3))^(t) Complete the following sentence about the monthly rate of change in the tiger population. Round your answer to two decimal places. Every month, the number of tigers decays by a factor of

Bytelearn · Accepted Answer

Understand function and task: Understand the given function and what is asked. The function N_(＂year ＂)(t) = 612 * (2/3)^t models the number of tigers over time, where t is the time in years. We need to find the monthly rate of change, which means we need to express t in months rather than years since there are 12 months in a year.Convert time to months: Convert the time from years to months. To find the monthly rate of change, we need to express t in terms of months. Since 1 year is equal to 12 months, we can say that t (in months) is equal to t/12 (in years).Rewrite function in months: Rewrite the function in terms of months. Let's denote M_(＂month ＂)(t) as the number of tigers after t months. Then we have: M_(＂month ＂)(t) = 612 * (2/3)^(t/12)Calculate monthly rate of change: Calculate the monthly rate of change. To find the monthly rate of change, we need to find the factor by which the population changes each month. This means we need to evaluate the expression (2/3)^(1/12), which is the base raised to the power of 1/12, representing one month.Evaluate (2/3)^(1/12): Evaluate the expression (2/3)^(1/12). Using a calculator, we find that (2/3)^(1/12) is approximately equal to 0.9438743126816935.Round result to two decimal places: Round the result to two decimal places. Rounding 0.9438743126816935 to two decimal places, we get approximately 0.94.Interpret monthly rate of change: Interpret the result. The factor 0.94 means that each month, the number of tigers decays by a factor of 0.94. This is the monthly rate of change.

Full solution

More problems from Multi-step problems with percents

Related topics