in 2011 a country\'s federal receipts (money taken in) totaled $2.36trillion. In
ID: 2850262 • Letter: I
Question
in 2011 a country's federal receipts (money taken in) totaled $2.36trillion. In 2013, total federal receipts were
$2.68 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 $12 trillion?
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 $12 trillion?
Explanation / Answer
general form of exponential function is y=aekt
1)in 2011, t=0
In 2011, total federal receipts were $2.36 trillion
2.36 =ae0
a=2.36
y=2.36ekt
In 2013, total federal receipts were $2.68 trillion
in 2013, t=2
2.68=2.36ek*2
ek*2=2.68/2.36
2k=ln(2.68/2.36)
k=(1/2)ln(2.68/2.36)
k=0.063578
f(t)=y=2.36e0.063578t
b)t=2015-2011=4
f(4)=y=2.36e0.063578*4
f(4)=3.04trillion
c)12=2.36e0.063578t
e0.063578t=12/2.36
0.063578t=ln(12/2.36)
t=[ln(12/2.36)]/0.063578
t=25.6
t=26
in the year 2011+26=2037 total federal receipts be $12 trillion
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