In 1995, the gross domestic product (gdp) of the united states was $7,398 billion. in 2000, it was $9,817 billion. (a) develop the exponential model that represents the nation's gdp. (write your model in terms of t, where t is the number of years after 1995. let p represent the gdp in billions. round the coefficient of t to seven decimal places.) (b) use the model to predict the gdp in 2004. (the actual 2004 gdp was $11,735 billion. round your answer to the nearest whole number.)

p(0) = 7398

p(5) = 9817

p(t) is the predicted GDP in billions in t years after 1995.

a) an exponential model for p(t)

b) p(9)

There are a number of ways to write exponential models. My favorite uses the given numbers exactly, so no rounding or approximation is necessary. This version gives

... p(t) = 7398·(9817/7398)^(t/5)

Then

... p(9) = 7398·(9817/7398)^(9/5) ≈ 12,310

If you want to use e as the base of your exponential function, then the exponent multiplier in e^(kt) becomes

... k = ln(9817/7398)^(1/5) ≈ 0.0565812

so the function is

... p(t) = 7398·e^(0.0565812t)

and

... p(9) ≈ 12,310

The GDP in 2004 is predicted to be 12,310 billion.

[editorial comment] It is not surprising that the estimate is a little high. The model assumes annual growth of 5.8%, which is a little higher than the long-term average. Over the 9 years from 1995 to 2004, the average was actually 5.26%

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have