Question

In 2011 a country's federal receipts (money taken in) totaled $2.03 trillion. In 2013, total federal receipts were $2.79 trillion. Assume that the growth of federal receipts, F, can be modeled by an exponential function and use 2011 as the base year (t=0). a) Find the growth rate k to six decimal places, and write the exponential function F(t), for total receipts in trillions of dollars. b) Estimate total federal receipts in 2015. c) When will total federal receipts be $15 trillion?

Answer 1

To find the growth rate and exponential function for total federal receipts, use the formula F(t) = F(0) * e^(kt). Plug in the values and solve the equations to find the growth rate, estimate federal receipts in 2015, and determine when receipts will reach $15 trillion.

Step-by-step explanation:

To find the growth rate k and the exponential function F(t), we can use the formula for exponential growth: F(t) = F(0) * e^(kt). Given that F(0) is $2.03 trillion in 2011 and F(t) is $2.79 trillion in 2013, we can set up the equation:

$2.79 = $2.03 * e^(k * 2)

Solving this equation will give us the growth rate k to six decimal places.

b) To estimate total federal receipts in 2015, we can use the exponential function F(t) by plugging in the value of t as 4 (since 2015 is 4 years after 2011).

c) To find when total federal receipts will be $15 trillion, we can plug in F(t) = 15 into the exponential function and solve for t.

Learn more about Exponential growth