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 whe

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.

in progress 0
Maria 3 days 2021-10-12T08:28:29+00:00 1 Answer 0

Answers ( )

    0
    2021-10-12T08:29:35+00:00

    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

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )