hi, i've been working on my homework that's due tomorrow, and i'm nearly done, but these are the only problems i've had trouble with. all questions are non-calculator, so steps would be appreciated:

The graph of the function f(x)= 3e^x-4 has an asymptote of

a) x= -4
b) x= 3
c) y= -4
d) y= 3
e) y=x

What are the steps for solving this? i haven't been given a formula. isn't the first step to find ln of the equation? how do i go about doing that?

Radioactive substance decreases by 10% per hour. if there were 64 grams of the substance at time t=1, which of the following exponential functions models the amount, R, in grams of the substance as a function of the time, t, in hours?

a) R= 54(1.10)^t
b) R= 60(1.10)^t
c) R= 48.6(1.10)^t
d) R= 54(.90)^t
e) R= 60(.90)^t

The equation for the decay function is A(t)= a(1-r)^t, I believe. I came up with 1= 54(.90)^t as my answer, so that's d, but i am not completely sure..

k(x)= 4^x, then k(x-2)=

a) 1/16(4^x)
b) 1/2(4^x)
c) 4^x-16
d) 4^x-2
e) (1/16)^x

I know that since it is not asking for k(x)-2, d is definitely not a correct answer. k(x-2)= 4^(x-2), so what are the next steps??

I have this table of values:
x | -1 | 0
f(x)|-6 | -2
I need to make it into an exponential function. What are the steps I should take?
Choices are:
a) y= 2(-3)^x
b) y= -2(-3)^x
c) y= -2(3)^-x
d) y= 1(-6)^x
e) y= -1(6)^x

Population of students at school is modeled by function P(t)= 500(1.12)^t, where t is the number of years since 1995. With this model, by what % is the popilation of the school changing each year?

a) 400%
b) 112%
c) 88%
d) 12%
e) 4%

i'm guessing d, 12%, since this seems to be following the growth formula A(t)= a(1+r)^t, am I right?

i hope you can help, thank you!!!

2. I'll tackle a couple.

#1) Are there any values of x you CAN'T put into your function $\displaystyle f(x) = 3e^x -4$? Doesn't look like it - pretty much anything will work for x.

Are there any values you CAN'T get out for f(x)? Look at that e^x. Can it ever equal zero? Nope - an exponential function can never equal zero. That means 3e^x can't be zero, so 3^x - 4 can never be -4. Based on that, I choose c.

#3) You're right - you have $\displaystyle 4^{(x-2)}$. That's the same as:

$\displaystyle \frac{4^x}{4^2}$ (remember when you divide powers with the same base, you can subtract the exponents; thus, you can rewrite a difference of exponents as division - that sounds a little confusing, but hopefully makes sense).

I'll leave it to you to simplify the above.

#4) Since it's multiple choice, I would just try plugging in both x-values into each of your 5 choices and seeing which function works (i.e., gives you the correct f(x) values) for the information you're given.