Question

Population grows.

Answer 1

Population are often modelled by exponential functions

The population will reach 1000000 people after 26.5 years

The population function is given as:

$P(x) = 692600 \times 1.014^x$

When the population reaches 1000000 people, we have:

P(x) = 1000000

So, the equation becomes

$1000000 = 692600 \times 1.014^x$

Divide both sides by 692600

$1.444=1.014^x$

Take logarithm of both sides

$log(1.444)=log(1.014)^x$

Apply logarithm to both sides

$log(1.444)=xlog(1.014)$

Make x the subject

$x = \frac{log(1.444)}{log(1.014)}$

Solve the logarithms of 1.444 and 1.014

$x = \frac{0.15957}{0.00603}$

Divide

$x = 26.5$

The value of x, is the number of years the population reaches 1000000 people.

Hence, the population will reach 1000000 people after 26.5 years

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