Exponential Functios questions help?

1.

3^(x-2)=5^x

2^(x-2)=3^(x+1)

cant use log.

2. Lucas is hoping to take a vacation after he finishes university. To do this he needs $5000, he finishes with $3500 in an investment that pays 8.4 per year, compounded quarterly. how long will Lucas have to wait before he has enough money to go on vacation.

I did 3500*1.084^x/4 wrong results

Re: Exponential Functios questions help?

You can't solve either of question 1 without logarithms.

Re: Exponential Functios questions help?

Hello, skg94!

Quote:

$\displaystyle 1(a)\;3^{x-2}\:=\:5^x$

. $\displaystyle (b)\;2^{x-2}\:=\:3^{x+1}$

Can't use log. . Then they can't be solved.

Quote:

2. Lucas is hoping to take a vacation after he finishes university. .To do this he needs $5000.

He has $3500 in an investment that pays 8.4% per year, compounded quarterly.

How long will Lucas have to wait before he has enough money to go on vacation?

The formula is: .$\displaystyle A \;=\;P(1 + i)^n$

. . where: .$\displaystyle \begin{Bmatrix} P &=& \text{principal invested} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$

We have: .$\displaystyle P = 3500,\;i = \frac{0.084}{4} = 0.021,\;n = 4x$

. . where $\displaystyle x$ is the number of years.

Then: .$\displaystyle 3500(1.021)^{4x} \:=\:5000 \quad\Rightarrow\quad (1.021)^{4x} \:=\:\tfrac{10}{7}$

Take logs: .$\displaystyle \ln(1.021)^{4x} \:=\:\ln\left(\tfrac{10}{7}\right) \quad\Rightarrow\quad 4x\ln(1.021) \:=\:\ln\left(\tfrac{10}{7}\right) $

Therefore: .$\displaystyle x \;=\;\frac{\ln(\frac{10}{7})}{4\ln(1.021)} \;\approx\;4.29\text{ years}$

Re: Exponential Functios questions help?

my answer says its 4.5

its nice to know the interest formula though, if i were to graph it which formula would i use?

3500(1+(.084/4)^4x ?

or 3500 * (1.021)^4x

well the thing is while i know how to do log, my test tomorrow will strictly be using expontential fuctions only, so i guess my teacher made a mistake in this review

Re: Exponential Functios questions help?

Why would you think that a test on exponential functions wouldn't include logarithms? Logarithms are the inverse functions of exponentials, and so MUST be used in many cases involving exponential functions, such as the ones above.

Re: Exponential Functios questions help?

Because the the teacher hasnt taught it so i cant be tested on something i havent been taught?

If he gives a test on lessons he hasnt even mentioned then how can i be expected to answer them.

I know log because i was told to do this using log, but seeing as how i wouldnt be able to use them on a quiz where i havent learned logs i decided to ask if there is a way without them, which there isnt