Question

The exponential model A=58.7e^0.02t 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 89 million.

Answer 1

Answer:

About 20.81 years

Step-by-step explanation:

89 million is the "final population" -- population after t years.

So, 89 million would be in "A" in the equation. Then we will have to solve for "t" by taking LN (natural logarithm). That is how we solve exponential equations.

So,

$A=58.7e^{0.02t}\\89=58.7e^{0.02t}\\\frac{89}{58.7}=e^{0.02t}\\1.5162=e^{0.02t}$

Now we recognize the exponential rule of:

Ln(e) = 1

and we use the property:

$Ln(a^b)=bLn(a)$

Now, we solve by taking Ln of both sides:

$1.5162=e^{0.02t}\\Ln(1.5162)=Ln(e^{0.02t})\\Ln(1.5162)=0.02tLn(e)\\Ln(1.5162)=0.02t\\t=\frac{Ln(1.5162)}{0.02}\\t=20.81$

So, population would be 89 million in about 20.81 years