Radioactive isotope #1
has been kept for 3.3 years. Originally, there were 100 grams and now there are 96.43 grams.

What is the half-life?
Round to the nearest year
What is the mystery element?
When will there be 1 gram left?
Round to the nearest year

Half-life = 63 years

Mystery element is Titanium-44

There will be 1 gram left after 419 years have passed

Step-by-step explanation:

In general the equation describing half-life is:

Where m is the final mass, m0 is the starting mass, t is the total elapsed time, and t(1/2) is the length of the half life. t / t(1/2) is actually the number of half-lives that have passed.

Anyways - all your questions can be answered using the above equation.

What is the half-life?

I subbed in the values we know from the question. In solving this I used the natural logarithm (but a log of any base will do - the goal is to bring down the exponent):

What is the mystery element?

Titanium-44, because it's half-life in the table is closest to the calculated half-life.

When will there be 1 gram left?

Again use the equation. This time the total time, t, is unknown. We can use the previously calculated half-life:

phosphate, calcium ion, chloride ion, neon atom

step-by-step explanation:

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.