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
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)=
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?
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?
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!!!