Question

After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S year(t), is modeled by the following function: S year(t)=25,000,000⋅(0.78)t Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places. Every decade, the number of species decays by a factor of

Answer 1

Answer:

Every decade, the number of species decays by a factor of 0.0834.

Step-by-step explanation:

Let be $S(t) = 25,000,000\cdot 0.78^{t}$, $\forall t \geq 0$. The decay rate per decay is deducted from the following relation:

$\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}$

$\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}$

$\frac{S(t+10)}{S(t)} = 0.78^{10}$

$\frac{S(t+10)}{S(t)} = 0.0834$

Every decade, the number of species decays by a factor of 0.0834.