The exponential model A=429e 0.024t 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 559 million.

In this question, we are asked to calculate the year at which the population of a country will be a certain amount given the exponential equation through which the equation proceeds.

Let’s rewrite the exponential function;

A = 429e^0.024t

Now here, our A is 559,000,000

t is unknown

Let’s substitute this value of A in the exponential equation;

559,000,000 = 429 * e^0.024t

559,000,000/429 = e^0.024t

1,303,030.303030303 = e^0.024t

Let’s take the logarithm of both sides to base e, we have;

ln(1,303,030.303030303) = ln(e^0.024t)

14.08 = 0.024t

t = 14.08/0.024

t = 587 years

Now, we add this to year 2003 and this gives year 2590

raphealnwobi raphealnwobi · Answer 2 · 2021-12-03T10:59:57+01:00

The population of the country will be 559 million in 2014.

An exponential growth is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

A represent the population of the country in millions t years after 2003.

Given the exponential model:

[tex]A=429e^{0.024t}[/tex]

At a population of 559 million:

[tex]559=429e^{0.024t}\\\\e^{0.024t}=1.303\\\\0.024t=0.2647\\\\t=11\ years[/tex]

The population of the country will be 559 million in 2014(2003 + 11).

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The exponential model A=429e 0.024t 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 559 million.

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The exponential model A=429e 0.024t 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 559 million.