In 2011 a country's federal receipts (money taken in) totaled $2.31 trillion. in 2013, total federal receipts were $2.83 trillion. assume that the growth of federal receipts, f, can be modeled by an exponential function and use 2011 as the base year (tequals0).
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 $10 trillion?

Using an exponential function, we have that:

a)

The growth rate is

The function is:

b)

The estimate for the total federal receipts in 2015 is of $3.47 trillion.

c)

Federal receipts will be of $10 trillion in 2025.

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Assume that the growth of federal receipts, F, can be modeled by an exponential function and use 2011 as the base year:

This means that the function for the amount in t years after 2011, in trillions of dollars, is:

In 2011 a country's federal receipts (money taken in) totaled $2.31 trillion.

Thus .

Item a:

In 2013, total federal receipts were $2.83 trillion, which means that , which is used to find k.

The growth rate is

The function is:

Item b:

2015 is 4 years after 2011, thus this is F(4).

The estimate for the total federal receipts in 2015 is of $3.47 trillion.

Item c:

This is t years after 2011, considering t for which F(t) = 10. Thus:

2011 + 14 = 2025.

Federal receipts will be of $10 trillion in 2025.

A similar problem is given at link

Step-by-step explanation:

An exponential equation can be written in the form

where a is the initial condition and b is the growth/decay rate.  It's growth if the number is greater than 1 and it's decay if the number is less than 1 but greater than 0.  Our initial conditions are, in coordinate form where 2011 is year 0:

(0, 2.31) (2, 2.83)

Use those to find the equation for our situation.  Always start out with the coordinate that has a 0 as x, since anything raised to the power of 0 is equal to 1. So we begin with the coordinate (0, 2.31):

so

2.31 = a

Now we use that a value along with the x and y from the other coordinate to come up with our growth or decay rate:

Divide both sides by 2.31 to begin to isolate the b:

and

so

b = 1.106846

That means that this is a growth rate (but you knew that already).

The equation then for this particular situation is:

That answers part a.

For part b, we will use that equation to find y when x = 4 (2015-2011 = 4):

Raise what's inside the parenthesis to the power of 4 to get:

y = 2.31(1.500889778) so

y = 3.47 trillion

For part c. we are looking for x when y = 10:

Divide both sides by 2.31 to get:

Take the natural log of both sides to enable us to bring the x down front:

Now divide both sides by the growth rate to get that

x = 14.434 or approximately 14 years after 2011 which is the year 2025.

the correct answer is a) "catholic church".

the proposals that liberals in mexico made during 1855 were particularly focused on a person's individual rights, such as the freedom of speech, the freedom of conscience, freedom of assembly, and the right to possess weapons.

when the constitution was formally published 2 years later (1857). it also contained an article which permitted education free from any religious influence, the removal of the catholic church institutional privileges, and the sale of property belonging to the church. all of these provisions were clearly against the catholic church interests.  

believe it or not anna is correct good job anna give me a fist bump there u go gal