A country's population and the growth rate in 2011 are given below. Assume that the growth rate remains the same from year to year. Use this information and an exponential model to estimate the country's population in the specified year. population $$ =158 $$ million; growth rate $$ =-0.53 $$ percent, year, 2018 The size of the population in the 2018 will be about $$ \square $$ million. (Round to the nearest hundredth as needed.)

Question

UpStudy AI · Accepted Answer

Let $$ P_0 = 158 $$ million in 2011 and the yearly growth rate is $$-0.53\%$$. Converting the percentage to a decimal gives
$$
r = -0.0053.
$$

For an exponential model with continuous growth, the population after $$ t $$ years is given by
$$
P(t) = P_0 e^{rt}.
$$
Here, $$ t = 2018 - 2011 = 7 $$ years. Thus,
$$
P(7) = 158 \times e^{-0.0053 \times 7}.
$$
Multiplying in the exponent:
$$
-0.0053 \times 7 = -0.0371.
$$
So,
$$
P(7) = 158 \times e^{-0.0371}.
$$
Calculating $$ e^{-0.0371} $$, we get approximately
$$
e^{-0.0371} \approx 0.9636.
$$
Therefore,
$$
P(7) \approx 158 \times 0.9636 \approx 152.21.
$$

The estimated population in 2018 is about $$ \boxed{152.21} $$ million.
The estimated population in 2018 is about 152.21 million.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Algebra Questions