Question

The expression 11(1.022)* models the per capita gross domestic product (GDP) of the US, in thousands of

Answer 1

Answer:

$y = a (b)^t$

Where a represent the initial amount and b the rate of growth/decay for the model and the time in  years since 1950.

For this case the value of b is given by:

$b = 1.022$

And if we solve for r the rate of growth we got:

$1.022 = 1+ r$

$r = 1.022-1= 0.022$

The answer for this case would be: 1.022 represent the growth factor for the GDP since 1950 (because b >1) and each year the GDP increase by a factor of 1.022

Step-by-step explanation:

For this case we are ssuming that we can model the GDP gross domestic product (GDP) of the US, in thousands of  dollars with the folllowing function:

$GDP = 11 (1.022)^t$

And we can see that this formula is governed by the exponential model formula given by:

$y = a (b)^t$

Where a represent the initial amount and b the rate of growth/decay for the model and the time in  years since 1950.

For this case the value of b is given by:

$b = 1.022$

And if we solve for r the rate of growth we got:

$1.022 = 1+ r$

$r = 1.022-1= 0.022$

The answer for this case would be: 1.022 represent the growth factor for the GDP since 1950 (because b >1) and each year the GDP increase by a factor of 1.022