# Exponential Growth etc

1. Oct 15, 2006

### thomasrules

the question is how do I solve

$$(1.024)^t=2.857$$

and find "t" without using logarithms

2. Oct 15, 2006

### Office_Shredder

Staff Emeritus
You don't.

You could just guess and check... i.e., what is it if t=2, 3, 4, etc. If at t0 the LHS is under 2.857, and at t1 the LHS is over, you know that the t you're looking for is between the two values.

There's probably an algorithm you can use or something

3. Oct 15, 2006

### HallsofIvy

Staff Emeritus
Why would you not want to use logarithms? That's what logarithms are for! Other than that, use the "midpoint algorithm". Find two values of t that give one value lower than 2.857 and one larger (hint: try 44 and 45), then try half way between. Keep going "half way" between one number that gives less than 2.857 and one that gives more than, reducing the interval each time.

4. Oct 15, 2006

### Checkfate

Gotta just guess and guess and guess. It's 44.2633... lol :).

But... Just so you know in the future. $$A^{x}=A^{y}$$ can be rewritten as x=y.

Edit, in this case $$(1.024)^{t}=(1.024)^{44.2633}$$ So $$t=44.2633$$

Last edited: Oct 15, 2006
5. Oct 15, 2006

### thomasrules

yea i know that rule thanks guys

6. Oct 15, 2006

### thomasrules

yea ok but wait how do u find the inverse of like

$$y=3(2)^x$$ or $$y=(x)^{1/3}$$

whats the formula is not in the book

Last edited: Oct 15, 2006
7. Oct 15, 2006

### thomasrules

i suck at this tex stuff i can't get the x^(1/3) and I wrote the y=3(2)^x first and it appeared second...wtf

8. Oct 15, 2006

### mk_gm1

Do you mean inverse? The inverse of a function basically just means swap x and y around. So $$y=x^{1/3}$$ goes to $$x=y^{1/3}$$...

Last edited: Oct 15, 2006