Question

An environmental study of a certain metropolitan region indicates that given population x (in thousands), the average daily level of carbon monoxide in the air is given by c(x) = 0.5x + 2c ( x ) = 0.5 x + 2 parts per million. The population of the region after t years is modeled by the formula x(t) = 10 + 0.1t^2x ( t ) = 10 + 0.1 t 2. When will the carbon monoxide level reach 7.8 parts per million? Group of answer choices 3 years 5 years 6 years 4 years

Answer 1

In 4 years the carbon monoxide level reach 7.8 parts per million.

Step-by-step explanation:

The average daily level of carbon monoxide in the air is given by :

`c(x) = 0.5x + 2` parts per million..[1]

The population of the region after t years is modeled by the formula :

`x(t) = 10 + 0.1t^2`...[2]

If level of carbon monoxide level reach 7.8 parts per million in t years.

Using [1] to calculate value of x.

c(x)= 7.8 parts per million

c(x) = 0.5x + 2 parts per million

7.8 parts per million = (0.5x + 2 ) parts per million

Solving for x , we get ;

x = 11.6

Using [2] to calculate value of t.:

x(t) = 11.6

`11.6 = 10 + 0.1t^2`

Solving for 't' we get ;

t = 4 years

In 4 years the carbon monoxide level reach 7.8 parts per million.