Polonium-210 is a radioactive substance with a half life of 138 days. if a nuclear facility is handling 265 grams of polonium-210, then how many grams of polonium-210 will be left after 250 days.

The half life is 138 days, meaning exactly half of the material will decay after this time. Use this information to find the decay factor :

Then after 250 days, there will be

grams left.

Step-by-step explanation:

The amount of substance decreases by 50 % every half-life.

Thus, 50 % of the substance remains at the end of each half-life.

The exponential function is

where x = the number of half-lives.

Data:

a₀ = 265 g

t = 250 da

Calculations:

(a) Calculate x

(b) Calculate a

we will first plot all x,y points on graph as shown in attachment.

(a) as you can see in attachment we get straight line so we can say yes number of employess are correlated to number of products produced monthly. they are linearly correlated by linear function

(b) as its straight line so it has to be linear function

to write linear function equation we will select any two random points on graph here. lets say (0,120) and (10,200)

so first find slope using slope formula

for two points given and

so for point (0,120) and (10,200) we will have slope as

equation of line is given by

so lets plug 8 in m place , 0 in place and 120 in place in formula

y - 120 = 8(x - 0)

y - 120 = 8 (x)

now solve for y and get y by itself

y - 120 = 8x

y - 120 + 120 = 8x + 120

y = 8x +120

so thats the equation of function that best fits the data

(c) slope = 8 indicates rate of increase or how fast is the number of products produced monthly is changing with number of employees.

y intercept is point where line cuts y axis which is at (0,120). so that means for 0 number of employees (x) we have number of products produced monthly(y) as 120. so intially there were 120 products