Question

What change(s) should Sylvia make to the equation to find the value of t in the above scenario?

Answer 1

Answer:

Option (D).

Step-by-step explanation:

Initial population of the deer $P_{0}$ = 4800

Decrease in the population of the deer after every 8 years = $\frac{1}{2}\times (\text{Initial population})$

Decrease in population is an exponential process, so the expression representing population will be,

$P_{t}=P_{0}(1-r)^x$

Where $P_{t}$ is the population after 'x' slots of 8 years.

r = fraction of decrease in the population

x = $\frac{\text{Number of years}}{8}$

By substituting the values of r and x in the expression,

$P_{t}=P_{0}(1-\frac{1}{2})^{\frac{t}{8}}$

$P_{t}=4800(\frac{1}{2})^{\frac{t}{8}}$

Therefore, Sylvia should do few corrections in her expression.

(8) should be replaced by ($\frac{1}{2}$) and $\frac{t}{2}$ should be replaced by $\frac{t}{8}$.

Option D. will be the answer.