The mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e^ −0.1315 t .
1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities.
2. what is the initial amount of cobalt-60 in the sample?
2. how much cobalt-60 is left after 8.4 years? show your work.
3. what would be the y-intercept of the graph? what does it represent?
4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years?
5. discuss some “real-world” examples and uses of cobalt-60.

maybe i can

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240