In November 2010, a "tiger summit" was held in St....

In November $2010,$ a "tiger summit" was held in St. Petersburg, Russia. ${ }^{44}$ In 1900 , there were 100,000 wild tigers worldwide; in 2010 the number was 3200 . (a) Assuming the tiger population has decreased exponentially, find a formula for $f(t),$ the number of wild tigers $t$ years since 1900 . (b) Between 2000 and 2010 , the number of wild tigers decreased by $40 \% .$ Is this percentage larger or smaller than the decrease in the tiger population predicted by your answer to part (a)?

In November $2010,$ a "tiger summit" was held in St. Petersburg, Russia. ${ }^{44}$ In 1900 , there were 100,000 wild tigers worldwide; in 2010 the number was 3200 .
(a) Assuming the tiger population has decreased exponentially, find a formula for $f(t),$ the number of wild tigers $t$ years since 1900 .
(b) Between 2000 and 2010 , the number of wild tigers decreased by $40 \% .$ Is this percentage larger or smaller than the decrease in the tiger population predicted by your answer to part (a)?

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Key Concepts

Percentage Change and Model Comparison

Calculating the percentage change between two time intervals in an exponential decay context involves comparing the model’s outputs at those times. This comparison helps to determine the relative decrease over a period and to assess whether the predicted rate of decline aligns with observed percentage drops.

Exponential Decay Model

An exponential decay model describes processes where quantities decrease at a rate proportional to their current value. This model is generally written as f(t) = A·e^(kt), where A is the initial amount, t represents time, and k is the decay constant. It encapsulates the behavior of many natural decay processes, including population decline under certain conditions.

Decay Constant Calculation

Determining the decay constant involves using known values of the model at different time points to set up an equation that can be solved with logarithms. By substituting the initial amount and the amount at a later time into the model, one can solve for k, which characterizes the rate of decay.

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