Question

The sales in thousands of dollars that Terrific Toys makes during one month can be approximated by the functions S(x)=2x³-2x²+4x, where x represents the number of days after the first day of the month. About how many days will it take the store to make $50,000?

Answer 1

The days will it take the store to make $50,000 in a whole number are:

• 30 days.

Explanation:

Remember that x represents the number of days, so, you must replace different values in the formula until you obtain a value of $50,000, in this form:

• S(x)= 2x³-2x²+4x
• S(1)= 2*1³-2*1²+4*1
• S(1)= 4 ($4).

So, I'll show you that the value that you need is 30 in a whole number.

• S(30)= 2*30³-2*30²+4*30
• S(30)= 52,320 ($52,320)

I know that the value exceeds the amount of $50,000, but if you use just a day before:

• S(29)= 2*29³-2*29²+4*29
• S(29)= 47,212 ($47,212)

How you can see, if you use 29 days, the value doesn't reach $50,000, by this reason, you must use 30 days to reach it.