Could you help me?

Question

How do you simplify this?
Do you first divide 0.0067 with each term?

80,000 = [ 1 - (1.0067)^(-12 t) / 0.0067 ]

To make it clear, the first part in the brackets [ ] divided by 0.0067

I suppose you may have to use logarithms...

Answer 1

When you say "the first part in the brackets [ ] divided by 0.0067," I'm assuming you mean:

80,000 = [ 1 - (1.0067)^(-12 t) ] / 0.0067

Multiply both sides by 0.0067:

586 = 1 - (1.0067)^(-12 t)

Subtract 1 from both sides, then multiply both sides by -1:

-585 = (1.0067)^(-12 t)

At this point you're pretty much stuck, because there is no exponentiation that yields a negative number: there's no power you can raise 1.0067 to, to get -585. (If I didn't move the brackets, and solved the equation as you wrote it, the same problem is encountered, but with slightly different numbers.)

Assuming there's a sign error in there somewhere, assume it's positive 585 instead:

585 = (1.0067)^(-12 t)

Take the log of both sides:

ln(585) = ln( (1.0067)^(-12 t) )

Use "ln(a^b) = b * ln(a)" to break out -12t:

ln(585) = -12 t * ln(1.0067)

Solve from there using a calculator:

6.3716 = -12 t * 0.006678
6.3716 / 0.006678 = -12 t
954.169 = -12 t
-79.514 = t

Answer 2

Yep