Question

The expression 11(1.022)^t11(1.022)


t


11, left parenthesis, 1, point, 022, right parenthesis, start superscript, t, end superscript models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since 195019501950.

Answer 1

Answer:

We have the expression

11*(1.0022)^t

That represents (in thousands) the per capita gross domestic product in the US since 1950.

This means that our function

GDP(t) = 11*(1.0022)^t

then, for t = 0 we obtain the GDP in the year 1950

GDP(0) = 11, in 1950 the GDP were 11 thousands.

If we want to calculate it today, we have:

GDP(70) = 11*(1.0022)^70 = 11.27 thousands.

This equation is an exponential growth of the form A*r^n

where A is the initial value, r is the rate of growth, and n is the variable.

We can analyze r and calculate r - 1 to get the portion that grows each year, this is

1.0022 - 1 = 0.0022

If we multiply it by 100%, we have:

0.0022*100$ = 0.22%

This means that the GDP increases by 0.22% each year.