Question

PLZ HELP ALGEBRA!!!!
AND PLZ SHOW WORK

Answer 1

Answer:

Step-by-step explanation:

n is the number of times the interest compounds per year.  If the interest in this problem only compounds once per year ("annually"), then n = 1 and you'd be just as well off to use the formula:

$A=P(1+r)^t$

When n = 1, r/n is just r.  But I'll show you using the formula they want you to use; it's the same anyways.

For us, P = 500, r = .015, n = 1.  Filling that into the formula:

$A=500(1+\frac{.015}{1})^{(1)(t)}$ which simplifies down to

$A=500(1+.015)^t$ and

$A=500(1.015)^t$  (see what I meant about not having to use the formula with "n" in it if n  1?)

That formula is the answer to part a.  For part b, we are to find how long it takes for the account to reach $800.  $800 goes in for A:

$800=500(1.015)^t$

Begin by dividing both sides by 500 to get:

$1.6=(1.015)^t$

The only way to bring that t down from its current exponential position is to take the natural log of both sides.  I will do that and at the same time apply the power rule for logs which says the exponent will come down out in front of the log:

$ln(1.6)=tln(1.015)$

Divide both sides by ln(1.015):

$\frac{ln(1.6)}{ln(1.015)}=t$

Do this on your calculator to find that

t = 31.5 years