# Exponential Growth for Pre-Calculus

Hi everyone.

My final is coming up for Precalc, and I'm studying my butt off.

I was really needing help with this Exponential Growth Equation to find variable t.

8.0e^(.033t) = 59.8e^(.001t)

(8 times e to the .033t equals 59.8 times e to the .001t)

I would greatly appreciate this because I'm stressing out for my finals. I have always been bad at this stuff

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CRGreathouse
Homework Helper
Just take the logarithm of both sides and it's easy to solve.

Just take the logarithm of both sides and it's easy to solve.
I know it sounds like I'm asking you to do it for me, but I really don't know where to begin. I'm confuzed because of the coefficients, because i can just natural log both sides if there weren't any.

If you can please guide me good sir, I KNOW I can do the rest of this subchapter by myself. Thanks a bunch

Just take the logarithm of both sides and it's easy to solve.
I know it's simple for you, but I swear it's so complicated for me. Please, this would really help me my kind sir

Integral
Staff Emeritus
Gold Member
What do you know about logs?

Review the basic laws, look especially at logs and multiplication. Also study the relationship between e and ln.

What do you know about logs?

Review the basic laws, look especially at logs and multiplication. Also study the relationship between e and ln.
I know about logs my good sir. It's just this one problem tripping me up. I just really need someone to show me how its done, and your help will defaintely be appreciated. Should i make one side equal zero? i just dont know,

will someone please help, this is the last problem i need and im done with this sub chater

Please, I really need help with this.

I have to solve for t here.

8.0e^( .033t ) = 59.8e^ (.001t)

Please, i just really need you to show me how this is done.

Borek
Mentor

exey = ex+y

exey = ex+y
I know that, but this is a weird one with weird coefficients. Please just walk me through this. gosh, im stressing out already

Just take the logarithm of both sides and it's easy to solve.
So CRGreathouse is suggesting to do this:

$$8.0e^{.033t} = 59.8e^{.001t}$$

$$\ln{(8.0e^{.033t})} = \ln{(59.8e^{.001t})}$$

Tell us what to do next.

01

so will it then turn into

ln 8.0 (.033t) = ln 59.8 (.001t)

Please ive been wait all day just to solve this one dang problem.

Integral
Staff Emeritus
Gold Member
so will it then turn into

ln 8.0 (.033t) = ln 59.8 (.001t)

Please ive been wait all day just to solve this one dang problem.
No, You need to use the laws for logs and multiplication.

No, You need to use the laws for logs and multiplication.
integral, i beg of you. i just really need someone to help me with this mroe in depth. i've been waiting all day, i would really appreciate it integral. please

would someone pklease help me. Im begign you guys. I need help with this. geeze

im begging yiou guys

Integral
Staff Emeritus
Gold Member
We need to see some effort on your part. Show me that you have even tried to apply the hints you have been given.

Your problem is of the form:

$$A e^x = B e^y$$
So taking the ln:
$$ln(A e^x) = ln (B e^y)$$

since ln(a * b ) = lna + lnb
$$lnA + ln(e^x) = lnB + ln(e^y)$$

Can you finish?

We need to see some effort on your part. Show me that you have even tried to apply the hints you have been given.

Your problem is of the form:

$$A e^x = B e^y$$
So taking the ln:
$$ln(A e^x) = ln (B e^y)$$

since ln(a * b ) = lna + lnb
$$lnA + ln(e^x) = lnB + ln(e^y)$$

Can you finish?
Integral, thank you kind sir.

Let's see here.

Yes sir.

Looks like it will be

ln 80 + .033t = ln 59.8 + .001t

From there

ln 80 - ln 59.8 = .001t - .033t

ln 80 - ln 59.8 = -.032
then divide and use a calculatro

something isnt adding up quite right sir, im getting a negattive numbe[/I]

wait, edit, it's ln 8 not 80. Thank you integral YOU ARE SO NICE. thank u so much.

Last edited:
HallsofIvy