In 2011 a country's federal receipts (money taken in) totaled $\$ 2.12$ trillion. In 2013 , total federal receipts were $\$ 2.63$ 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 $\$ 7$ trillion? a) Find the growth rate $k$. \[ k= \] (Do not round until the final answer. Then round to six decimal places as needed.)

Step 1 ：Given that the federal receipts in 2011 (base year) is $2.12 trillion, and in 2013 it is $2.63 trillion, we can model the growth of federal receipts, $F$, by an exponential function with 2011 as the base year $(t=0)$.

Step 2 ：The general form of an exponential function is $F(t) = F_0 * e^{kt}$, where $F_0$ is the initial amount, $k$ is the growth rate, and $t$ is the time.

Step 3 ：Substitute $F_0 = 2.12$, $F(2) = 2.63$, and $t = 2$ into the exponential function and solve for $k$.

Step 4 ：By solving, we find that the growth rate $k$ is approximately $0.107784$ to six decimal places.

Step 5 ：Substitute $k$ into the exponential function, we get $F(t) = 2.12 * e^{0.107784t}$.

Step 6 ：\(\boxed{0.107784}\) is the growth rate $k$ and the exponential function $F(t)$ for total receipts in trillions of dollars is $F(t) = 2.12 * e^{0.107784t}$.