Question

A(x) = -0.015x^3+1.05xA ( x ) = − 0.015 x 3 + 1.05 x gives the alcohol level in an average person's blood x hrs after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk.

Would an average person be legally drunk after 4 hours?

Answer 1

Yes

Explanation:

the function that gives the alcohol level is:

`A ( x ) = - 0.015 x^3 + 1.05 x`

where x is the number of hours.

we need to know if after 4 hours an average person is legally drunk, thus:

`x=4`

and we substitute this in the function:

`A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)`

solving these operations we obtain:

`A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2`

`A(4)=3.24`

the alcohol level after 4 hours is 3.24.

Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.