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Select the correct answer.

For the next five years, a dairy company wants to increase its daily milk processing capacity (in gallons) according to the equation [tex]y = x^6 - 9x^4 + 70x^2[/tex], where [tex]x[/tex] is the number of years. How many years will it take until the company can process 630 gallons of milk in a day?

A. 2 years
B. 3 years
C. 4 years
D. 5 years

Answer :

To determine how many years it will take for the dairy company to process 630 gallons of milk daily, we start by using the given equation for the milk processing capacity, which is:

[tex]\[ y = x^6 - 9x^4 + 70x^2 \][/tex]

Here, [tex]\( y \)[/tex] represents the processing capacity in gallons, and [tex]\( x \)[/tex] is the number of years.

We want to find the value of [tex]\( x \)[/tex] when [tex]\( y = 630 \)[/tex] gallons. So we set up the equation:

[tex]\[ x^6 - 9x^4 + 70x^2 = 630 \][/tex]

Now, let's solve this equation to find the value of [tex]\( x \)[/tex].

After solving the equation for the possible number of years, we find that:

[tex]\[ x = 3 \][/tex]

This means that it will take 3 years for the company to reach a daily processing capacity of 630 gallons of milk.

Thus, the correct answer is:

B. 3 years

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