Question

The total assets of bond mutual funds (in trillions of dollars) are approximated by f left parenthesis x right parenthesis equals negative 2.29 plus 1.423 ln x f(x)=−2.29+1.423lnx (x greater than or equals ≥10), where x equals =10 corresponds to 2000. (a) What were the total assets in 2003 2003 and 2008 2008? (b) If this model remains accurate, find the year in which total assets will reach $ 2.25 2.25 trillion.

Answer #1

(a)

Total assets f(x) is given by:

(i)

For 2003:

Substituting x = 13, we get:

So,

Answer is:

**1.3599** trillions of dollars

(ii)

(i)

For 2008:

Substituting x = 18, we get:

So,

Answer is:

**1.8230** trillions of dollars

(b)

For f(x) = 2.25, substituting, we get:

i.e.,

So, we get:

So,

x = 24.2992

So, year = 2034

So,

Answer is:

**2034**

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