Enter the given values into the equation and solve.
5800 = 4100e^(k*40)
Divide both sides by 4100 and simplify:
58 / 41 = e^(k*40)
Remove e by taking the logarithm of both sides:
ln(58/41) = k *40
Divide both sides by 40:
k = ln(58/41)/40
k = 0.00867
Now for the population to double set up the equation:
2*4100 = 4100e^kt
The 4100 cancels out on both sides:
2 = e^kt
Take the logarithm of both sides:
ln(2) = k*t
Divide both sides by k
t = ln(2) /k
replace k with the value from above:
t = ln(2) / 0.00867
t = 79.95
Rounded to the nearest tenth = 80.0 hours to double.
Answer:
Step-by-step explanation:
To answer the question, we first need to find the constant k, using the given information and the expression.
[tex]P=4100e^{kt} \\5800=4100e^{k(40)} \\\frac{5800}{4100}=e^{40k}\\e^{40k}=1.41\\lne^{40k}=ln1.41\\40k=0.34\\k=\frac{0.34}{40}\approx 0.0085[/tex]
Now that we have the constant. We can find the time it would take to double the population which would be 11600:
[tex]P=4100e^{kt}\\11600=4100e^{0.0085t}\\\frac{11600}{4100}= e^{0.0085t}\\e^{0.0085t}=2.83\\lne^{0.0085t}=ln2.83\\0.0085t=1.04\\t=\frac{1.04}{0.0085}\approx 122.35[/tex]
Therefore, it would take around 122 hours to double the population.
