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