Question

A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t)=(493)4 ^1/2, where t represents the number of years from the time of introduction. What is the quadrupling-time for this population of deer?

Answer 1

The answer is "2 years".

Explanation:

Given:

`\to P(t) = 493*4^{(t)/(2)}`

when t=0

`P(0) = 493*4^{(0)/(2)}\\\\`

`= 493*4^0\\\\= 493* 1\\\\= 493 \\`

Calculating the quadrupling time:

`\to P(t) = 4 * P(0) \\\\`

`= 4* 493 \\\\= 1972`

Solving

`\to 1972= 493*4^{(t)/(2)} \\\\\to 4 = 4^{(t)/(2)}\\\\\to (t)/(2) = 1\\\\\to t = 2\ years \\\\`