Question

For the years since 2001, the percent p of high school seniors who have tried marijuana can be considered as a function of time t according to p = f(t) = 0.17t2 − 2.61t + 52.64 where t is the number of years past 2000.† In what year after 2000 is the percent predicted to reach 75%, if this function remains valid?

Answer 1

Answer:

21 years after 2000 = 2021

Step-by-step explanation:

p = f(t) = 0.17t2 − 2.61t + 52.64

P = 75%= 75

0.75 = 0.17t2 − 2.61t + 52.64

0.17t2 − 2.61t + 52.64-75=0

0.17t2 − 2.61t – 22.36=0

Divide through by 0.17

0.17t2 − 2.61t -22.36=0

t2 – 15.29t – 131.53=0

using the quadratic formula

x=(-b±√(b^2-4ac))/2a

a =1, b = -15.29 , c=-131.53

Insering the values of a,b,c into the quadratic formula above

x=(15.29±√(15.29)^2+4*1*131.53))/(2*1)

x=(15.29±27.55)/(2*1)

t=21.5 or -6.124

Discard the negative value

t=21.5

Answer 2

Answer:

The year 2021.

Step-by-step explanation:

75% here means a the answer to our function is 75.

Thus, f(t) = 75

Now let's solve the equation for the variable t:

$75 = 0.17t^2 - 2.61t + 52.64$

$0.17t^2-2.61t-22.36= 0$

Solving for t using the quadratic formula we get:

t1  = 21.477

t2 = -6.124

As t is the number of years after 2000, and t can not be less than 0, our answer is t1.

This mean the percent is predicted to reach in the middle of the year 2021.

converting the number 0.477 to months we get: 0.477*12 = 5.72

This means the middle of may.

So our answer is May, 2021. And the year is just 2021.