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From 1945 to 2008 , one country's per capita gross domestic product (GDPPC) increased about
6% per year, ending at
$19,600. For the next few years, the growth slowed to an increase of about
$1,300 per year. To the nearest dollar, how much less did the GDPPC grow during the next 6 years than it would have if it had maintained its earlier growth rate?

From $1945$ to $2008$ , one country's per capita gross domestic product (GDPPC) increased about $6 \%$ per year, ending at $\$ 19,600$ . For the next few years, the growth slowed to an increase of about $\$ 1,300$ per year. To the nearest dollar, how much less did the GDPPC grow during the next $6$ years than it would have if it had maintained its earlier growth rate?

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Understanding integers

Full solution

Q. From

1945

to

2008

, one country's per capita gross domestic product (GDPPC) increased about

6 \%

per year, ending at

\$ 19,600

. For the next few years, the growth slowed to an increase of about

\$ 1,300

per year. To the nearest dollar, how much less did the GDPPC grow during the next

6

years than it would have if it had maintained its earlier growth rate?

Calculate GDPPC growth: Calculate the GDPPC growth for the next $6$ years at the earlier growth rate of $6\%$ per year. $\newline$ The formula for exponential growth is $P = P_0(1 + r)^t$ , where $P_0$ is the initial amount, $r$ is the growth rate, and $t$ is the time in years. $\newline$ $P_0 = \$19,600$ , $r = 6\%$ or $0.06$ , and $t = 6$ years.
Perform calculation for earlier growth rate: Perform the calculation for the earlier growth rate. $\newline$ $P = 19600(1 + 0.06)^6$ $\newline$ $P = 19600(1.06)^6$ $\newline$ $P \approx 19600 \times 1.4185$ $\newline$ $P \approx \$(27803.60)$
Calculate GDPPC growth at slowed rate: Calculate the GDPPC growth for the next $6$ years at the slowed growth rate of $\$1,300$ per year. $\newline$ The linear growth is calculated by adding the annual increase to the initial amount for each year. $\newline$ $P = P_0 + (\text{increase per year} \times \text{number of years})$ $\newline$ $P = 19600 + (1300 \times 6)$ $\newline$ $P = 19600 + 7800$ $\newline$ $P = 27400$
Calculate difference in GDPPC growth: Calculate the difference in GDPPC growth between the earlier growth rate and the slowed growth rate. $\newline$ Difference = GDPPC at earlier growth rate - GDPPC at slowed growth rate $\newline$ Difference = $27803.60$ - $27400$ $\newline$ Difference $\approx$ $\$403.60$

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