Answer
Explanation
Using the formula for the population growth:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]
where P₀ is the initial population, r is the rate of growth, and t is the time.
From the given information, we know that:
• P₀ = 10
,
• r = 0.2
1.
And we are asked to find P(50) (when t = 50), thus, by replacing the values we get:
[tex]P(50)=10\cdot(1+0.20)^{50}[/tex][tex]P(50)\approx91004.3815[/tex]
2.
For the population to double, this would mean that P(t) = 2P₀. By replacing this we get:
[tex]2P_0=10e^{0.20t}[/tex][tex]2(10)=10e^{0.20t}[/tex][tex]20=10e^{0.20t}[/tex][tex]\frac{20}{10}=e^{0.20t}[/tex][tex]\ln\frac{2}{1}=\ln e^{0.20t}[/tex][tex]\ln2=0.20t[/tex][tex]t=\frac{\ln2}{0.20}\approx3.5days[/tex]
