Question #273713

N(t)=2400000e^0.03t

What time is required for the population to tripple if N is the population size at time while t is the number of years

Expert's answer

"N=2400000e^{0.03t_1} \\;\\;\\;(1) \\\\\n\n3N = 2400000e^{0.03t_2} \\;\\;\\;(2)"

"(t_2 -t_1)" is time required for the population to tripple

Divide (2) by (1):

"\\frac{3N}{N} = \\frac{2400000e^{0.03t_2}}{2400000e^{0.03t_1}} \\\\\n\n3 = \\frac{e^{0.03t_2}}{e^{0.03t_1}} \\\\\n\n3 = e^{0.03(t_2-t_1)} \\\\\n\nln(3) = 0.03(t_2-t_1) \\\\\n\n(t_2-t_1) = \\frac{ln(3)}{0.03} = \\frac{1.098}{0.03} = 36.6 \\; years"

Answer: 36.6 years

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