Math Work Problem

Question

The exponential model A=684.9e^0.022t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 1040 million. (round to the nearest year as needed.) 

 

The population of the country will be 1040 million in ?  

Answer 1

1040 million = 684.9 e^0.022t
1.040 x 10¹² = 684.9 e^0.022t
1.040 x 10¹² = (6.849 x 10² ) e^0.022t
0.151847 x 10¹⁰ = e0.022t
ln (0.151847 x 10¹⁰) = ln e0.022t
ln (0.151847 x 10¹⁰) = 0.022t ln e
ln 0.151847 +10 ln 10 = 0.022t
-1.88488 + 10 (2.30)= 0.022t
21.1151 = 0.022t
959.77 = t

 

 

The target population is reached after 960 years.