Question

the expression $11(1.022)^t$ models the per capita gross domestic product (gdp) of the us, in thousands of dollars, as a function of the number of years since 1950.
what does 1.022 represent in this expression?
choose 1 answer:
a the maximum per capita gdp occurred 1.022 years after 1950.
b the per capita gdp in the us is multiplied by approximately 1.022 each year.
c the per capita gdp in the us was $1022 in 1950.

Explanation:

The expression \( 11(1.022)^t \) is an exponential growth model, where the general form is \( P(t)=a(b)^t \), with \( a \) as the initial value, \( b \) as the growth factor (where \( b = 1 + r \), \( r \) is the growth rate), and \( t \) as time. Here, \( 1.022 \) is the base of the exponent, representing the factor by which the per capita GDP is multiplied each year. Option A is incorrect as the expression doesn't relate to a maximum time. Option C is incorrect because the initial value (when \( t = 0 \)) is \( 11 \) (thousand dollars), not related to \( 1.022 \) representing a dollar amount in 1950.

Answer:

B. The per capita GDP in the US is multiplied by approximately 1.022 each year.