Final answer:
To determine when the population was predicted to reach 25.9 million, we need to solve the equation A = 19.6e^(0.0138t) for t. The population was predicted to reach 25.9 million approximately 17.295 years after 2000.
Step-by-step explanation:
To determine when the population was predicted to reach 25.9 million, we need to solve the equation A = 19.6e^(0.0138t) for t.
First, divide both sides of the equation by 19.6 to isolate the exponential term: e^(0.0138t) = A/19.6. To get rid of the exponential term, take the natural logarithm (ln) of both sides:
ln(e^(0.0138t)) = ln(A/19.6).
By the properties of logarithms, the ln and e^( ) will cancel out, leaving us with 0.0138t = ln(A/19.6). Finally, divide both sides of the equation by 0.0138 to solve for t:
t = ln(A/19.6) / 0.0138.
Now, substitute the given population value of 25.9 million into the equation to find the corresponding time (t). Plug A = 25.9 million into the expression for t and solve using a calculator:
t = ln(25.9/19.6) / 0.0138 = 17.295 years.
Therefore, the population was predicted to reach 25.9 million approximately 17.295 years after 2000.
Learn more about Exponential growth