The growth in population of a city can be seen using the formula p(t) $\mathrm { p } ( \mathrm { t } ) = 2196 \mathrm { e } ^ { 0.005 \mathrm { t } }$ , where t is the number of years. According to this formula, how many years will it take the population to double its year 0 value? Round
To the nearest tenth of a year.
A) 138.6 yr
B) 104.0 yr
C) 277.2 yr
D) 69.3 yr

Question

Quizplus · Accepted Answer

The population will double when p(t) = 4392. Solving for t gives:4392 = 2196 * e^(0.005t)2 = e^(0.005t)ln(2) = 0.005tt = ln(2) / 0.005 ≈ 138.6 years

The Growth in Population of a City Can Be Seen p(t)=2196e0.005t\mathrm { p } ( \mathrm { t } ) = 2196 \mathrm { e } ^ { 0.005 \mathrm { t } }p(t)=2196e0.005t

The Growth in Population of a City Can Be Seen $\mathrm { p } ( \mathrm { t } ) = 2196 \mathrm { e } ^ { 0.005 \mathrm { t } }$