math:solving for an exponent.

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I can't get the right answer, where am I going wrong?
7.0x10^9= (6.7x10^9)(2.72^r*3)
1.04 = 2.72^r*3

When I solve for this, I get ln (1.40) = 0.03922 then 0.03922 / 3 = 0.0130
So my r equals 0.0130

BUT the teacher says the answer is
0.05 = r *3
0.02 = r

What did I do wrong? I am so confused!! Help please. Show steps

• math:solving for an exponent. -

is that 2.723r ?

then 1.0447=2.72^3r

Ln 1.0447=3r *ln 2.72

r= 1/3 (ln1.0447/ln2.72)= 0.0148574093

When you are dealing with logs, you need to keep as many digits as you can. You are correct.

• math:solving for an exponent. -

1.04 = 2.7^(3r)

ln 1.04 = 3r ln 2.72

but that still does not give .05 = 3r

Typo in problem?

• math:solving for an exponent. -

No. The math he did was handwritten. I guess he must have made a mistake because this is driving me nuts. Everything listed in my post is CORRECTLY copied from the piece of paper I got it on.

• math:solving for an exponent. -

Bob, thank you. I thought I was going insane there for a minute. I guess the professor made a mistake. We are all human (but it drives me crazy when I'm trying to study haha)