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In 1950, the per capita gross domestic product (GDP) of Australia was approximately
$1800. Each year afterwards, the per capita GDP increased by approximately
6.7%.
Write a function that gives the approximate per capita GDP
G(t) of Australia
t years after 1950. Do not enter commas in your answer.

G(t)=

In $1950$ , the per capita gross domestic product (GDP) of Australia was approximately $\$ 1800$ . Each year afterwards, the per capita GDP increased by approximately $6.7 \%$ . $\newline$ Write a function that gives the approximate per capita GDP $G(t)$ of Australia $t$ years after $1950$ . Do not enter commas in your answer. $\newline$ $G(t)=$

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Write exponential functions: word problems

Full solution

Q. In

1950

, the per capita gross domestic product (GDP) of Australia was approximately

\$ 1800

. Each year afterwards, the per capita GDP increased by approximately

6.7 \%

.

\newline

Write a function that gives the approximate per capita GDP

G(t)

of Australia

t

years after

1950

. Do not enter commas in your answer.

\newline

G(t)=

Convert to decimal: Write $6.7\%$ as a decimal. $\newline$ $6.7\% = \frac{6.7}{100} = 0.067$
Determine growth factor: Determine the growth factor $b$ for the per capita GDP. $\newline$ For exponential growth, $b > 1$ . $\newline$ Growth factor: $b = 1 + r$ , where $r$ is the rate of increase.
Calculate growth factor: Calculate the value of the growth factor $b$ using the rate of increase $r = 0.067$ . $b = 1 + r$ $b = 1 + 0.067$ $b = 1.067$
Identify GDP values: Identify the initial per capita GDP $a$ and the growth factor $b$ to write the exponential function. $\newline$ Initial per capita GDP $a$ : $\$1800$ $\newline$ Growth factor $b$ : $1.067$ $\newline$ The function will be in the form $G(t) = a(b)^t$ .
Write exponential function: Write the exponential function using the values of $a$ and $b$ . $G(t) = 1800(1.067)^t$

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