Question

A​ once-popular children's doll is slowly declining in popularity. The quartic function f(x)=0.002x⁴+0.025x³-0.364x²-7.243x+86.993, where x is the number of years since​ 1993, can be used to estimate the number of dolls of this type that were sold​ (in thousands) during a given year from 1993 to 2003. Estimate how many dolls were sold in 2000.

Answer 1

Solution-

According to question,​ the children's doll is slowly declining in popularity and the function yhat represents number of dolls of this type is

here x is the number of years since​ 1993 that be used to estimate the number of dolls of this type that were sold​ (in thousands) during a given year from 1993 to 2003.

Now, in year 2000, x = 2000 -1993 = 7

On putting x=7 in above function,we get

On simplifying it, we get

So, number of dolls that were sold in 2000 are 31.833 thousand or 31,833.

Hence, 31,833 dolls were sold in year 2000.