The 1985 1985 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atmosphere. The function f left parenthesis x right parenthesis equals 1000 left parenthesis 0.5 right parenthesis Superscript StartFraction x Over 30 EndFraction f(x)=1000(0.5) x 30 describes the amount, f(x), in kilograms, of a radioactive element remaining in the area x years after 1985 1985. If even 100 kilograms of the radioactive element remains in the atmosphere, the area is considered unsafe for human habitation. Find f( 40 40) and determine if the area will be safe for human habitation by 2025 2025.

Step-by-step explanation:

If I'm understanding this correctly, the rate of decay function is

and we want to solve for the amount of element left after x = 40 years.  That would make our equation

Multiply the repeating decimal by .5 to get

f(40) = 1000(.3968502631)

and f(40) = 396.85

So no, it's not safe for human habitation.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

answer: 193

explanation:

200-7 = 193