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From 1960 to 2010, a certain money stock measure was growing at the rate of approximately 43e(1/2)x billion dollars per decade, where x is the number of decades since 1950. Find the total increase in the money stock measure from 1960 to 2010. (Round your answer to the nearest billion dollars.)

Respuesta :

Answer:

1222 billion dollars.

Step-by-step explanation:

To find the total increase from 1960 to 2010, we need to find the growth of each decade and sum them all:

In the period 1960-1970, we have x = 1, and the growth is:

[tex]y(1) = 43e(1/2) = 70.895[/tex]

In the period 1970-1980, we have x = 2, and the growth is:

[tex]y(2) = 43e(2/2) = 116.8861[/tex]

The growth in the following 3 periods are:

[tex]y(3) = 43e(3/2) =192.7126[/tex]

[tex]y(4) = 43e(4/2) = 317.7294[/tex]

[tex]y(5) = 43e(5/2) =523.8472[/tex]

So the total growth in the period 1960 - 2010 is:

[tex]Total = y(1) + y(2) + y(3) + y(4) + y(5)[/tex]

[tex]Total = 70.895 + 116.8861+192.726+317.7294+523.8472[/tex]

[tex]Total = 1222.08\ billion\ dollars[/tex]

Rounding to the nearest billion dollars, we have a total of 1222 billion dollars.

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