How do you solve this problem?

Question

A radioactive substance is changing into another element [decaying] acc. to the formula: y = Ae raised to -0.3x ; where y is the amt. of material remaining after x years

1. How much is left after 5 yrs. if initial amount A is ninety grams?
2. Find the half-life of the substance in which A= ninety grams

Answer 1

1) we need to know the amt of material (y) after 5 years (x). Thus, you substitute x = 5 in the equation, and substitute A = 90g and solve the equation.

y = 90 x e^(-0.3(5))
I pressed my calculator and found the y to be approx 20.08g.

2)When a substance reaches it's half life it the amount of substance will be half its original amount. Hence, the amount of the element remaining = 45g = y. Again, substitute it as well as the A = 90g into the equation.

45 = 90 x e^(-0.3x)
0.5 = e^(-0.3x)
In 0.5 = -0.3x
x = (In 0.5)/ (-0.3)
I pressed my calculator and got approx 2.31years

I hope it's right, please double check on your own.

Answer 2

First one, plug and chug...
y = 90e^(-0.3*5)
y = 20 (to two sig figs)

Half life:
45 = 90e^(-0.3*x)
ln45 = ln90 + (-0.3*x)
x = 2.3 (to two sig figs)