First we need to know both the formula of A and B.
The formula of A is
C = 5 + 0.25p
with C representing total cost and p representing the amount of checks.
The formula of B is
C = 6 + 0.15p
with C representing total cost and p representing the amount of checks.
To find the point where A and B cost the same, we solve the following equation:
5 + 0.25p = 6 + 0.15p
Collecting terms gives us
-1 = -0.1p
Now we have to divide by -0.1 and we get.
10 = p
p = 10
So our answer: after 10 checks both accounts cost the same amount of money. Answer A.
I can't see how any of those formulas show exponential decay. (Did you type those correctly?)
The formula that will show the remaining amount correctly is:
ending amount = Bgng Amount / 2^n
where "n" is the number of haf-lives.
So, for example if half life = 4 hours and if we want to calculate the amount after 9 hours (that's 2.25 half-lives) then:
ending amount = Bgng Amount / 2^n
ending amount = 50 / (2^(9/4))
ending amount = 50 / 2^2.25
ending amount =
50 / <span><span><span>4.75682846
</span>
</span></span><span><span>ending amount =
</span>
10.5112 grams
</span>Looking at the graph, we see that's about right.