Question

The population growth of a community is modeled by the equation P (x) = 15,5580.4x + 1, where P (x) is population and x is time in years beginning with x = 0. When does the population double? Round to the nearest tenth of a year.

Answer 1

Answer:

The population will be double in 0.5 years.

Step-by-step explanation:

The population growth of a community is modeled by the equation $P(x) = 155580(4)^{x + 1}$, where P (x) is population and x is time in years beginning with x = 0.

Therefore, the population at x = 0 will be = $P(0) = 155580(4)^{0 + 1} = 622320$

If the population becomes double then we can write the equation as

$P(x) = 2 \times 622320 = 155580(4)^{x + 1}$

⇒ $4^{x + 1} = 8$

⇒ $2^{2(x + 1)} = 2^{3}$

⇒ 2(x + 1) = 3 {Comparing the power terms}

⇒ x + 1 = 1.5

⇒ x = 0.5 years.

Therefore, the population will be double in 0.5 years. (Answer)