Asked by Nissan GT-R R35 Nismo
A small nest of wasps has an exponential growth rate of 13% per month, if the nest currently has 5,000 wasps, the situation can be modeled by the equation w (t) = 5,000 (1.13)^t, where w is the number of wasps after time t months. Which of the following statements is true about the equation?
As t increases, w decreases slowly at first and then quickly
as t increases, w decreases quickly at first and then slowly
as t increases, w increases slowly at first and then quickly
as t increases, w increases quickly at first and then slowly
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"As t increases, w increases slowly at first and then quickly."
Reason: 1.13^t is exponential with base > 1, so w grows and its growth rate accelerates. Mathematically w'(t) = 5000 ln(1.13) (1.13)^t, which increases as t increases, so the function is increasing and concave up (slow at first, then faster).
Reason: 1.13^t is exponential with base > 1, so w grows and its growth rate accelerates. Mathematically w'(t) = 5000 ln(1.13) (1.13)^t, which increases as t increases, so the function is increasing and concave up (slow at first, then faster).
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