Math 30-1, exponential growth and decay

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kris.yarmak123

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IMG_20191202_192004~01.jpg
Hello. I am really terrible with the applications, and I would be very grateful if someone could help me to answer this question.
I have started with writing the equation y=0.9375^(x)
I checked if it passes through the point (0,1) and it does pass. Then I checked if it passes through the point (2, 0.0625) and it does not pass, so I tried to rewrite the equation as y=0.9375^(x/2) and y=0.9375^(2x)
....and none of the equations worked out
 
OK, so you clearly are not getting the correct power. So stop guessing. Let the power be tx and then solve for t.
Please show us your work.
 
Jomo said:
OK, so you clearly are not getting the correct power. So stop guessing. Let the power be tx and then solve for t.
Please show us your work.
Click to expand...

Y=0.9375^tx
0.0625=0.9375^2t
log(0.0625)/log(0.9375)=2t
42,96=2t
t=21.48
...like this?
 
No need to ask me. Just check to see if the 2 points work. Let us know how you make out.

Also put parenthesis around tx !
 
Jomo said:
No need to ask me. Just check to see if the 2 points work. Let us know how you make out.

Also put parenthesis around tx !
Click to expand...
Ok, thanks.
Y=0.9375^(tx)
0.0625=0.9375^(2t)
log(0.0625)/log(0.9375)=2t
42,96=2t
t=21.48
 
I don't understand the question, but I think there is another part you didn't picture that asks for something and I think that this something is the decay rate.
If I'm right then you should start from here:
[MATH]6.25\%=100\%\times (1-x)^{2}\iff 0.0625=1\times(1-x)^{2}[/MATH]
 
Jomo said:
So does it work?
Click to expand...
Ok I think I found a good way I guess
y=(1/2)^(2x)
It does pass through the points (0,1) and (2,0.0625)
OmarMohamedKhallaf said:
I don't understand the question, but I think there is another part you didn't picture that asks for something and I think that this something is the decay rate.
If I'm right then you should start from here:
[MATH]6.25\%=100\%\times (1-x)^{2}\iff 0.0625=1\times(1-x)^{2}[/MATH]
Click to expand...
There's no other part... Here's the whole pic of the questions IMG_20191202_192004.jpg
 
kris.yarmak123 said:
Ok I think I found a good way I guess
y=(1/2)^(2x)
It does pass through the points (0,1) and (2,0.0625)
Click to expand...
There is no question in #23; it tells you something but doesn't say what you are to find!

Your new work suggests that maybe you are asked (in the instructions for that set of exercises?) for the half-life. (But that would be 30 seconds, and you didn't mention a unit in the answer!)

Please tell us what it is that you are trying to find; if there are instructions for the exercises, show us that, and if the answer is not just the number 30, tell us that, too.
 
Dr.Peterson said:
There is no question in #23; it tells you something but doesn't say what you are to find!

Your new work suggests that maybe you are asked (in the instructions for that set of exercises?) for the half-life. (But that would be 30 seconds, and you didn't mention a unit in the answer!)

Please tell us what it is that you are trying to find; if there are instructions for the exercises, show us that, and if the answer is not just the number 30, tell us that, too.
Click to expand...
The answer says 30 sec.
 
Yes, that's right. There are several ways to determine this, depending on how you textbook presents it; but you've not only refused to tell us that you were asked for the half-life, you have never told us what form you are using for the equation, so it's really hard to help you.

One form I've seen is A = A0(1/2)^(t/T), where T is the half-life. Your exponent (as you correctly had it before) was 2t, which can be thought of as t/0.5, so the half-life is 0.5 minute = 30 seconds.

(Now that I look again, I see this form in your problem 27, with 5.7 as the half-life. So apparently I have correctly figured out what you are supposed to do.)
 

Dr.Peterson said:
Yes, that's right. There are several ways to determine this, depending on how you textbook presents it; but you've not only refused to tell us that you were asked for the half-life, you have never told us what form you are using for the equation, so it's really hard to help you.

One form I've seen is A = A0(1/2)^(t/T), where T is the half-life. Your exponent (as you correctly had it before) was 2t, which can be thought of as t/0.5, so the half-life is 0.5 minute = 30 seconds.

(Now that I look again, I see this form in your problem 27, with 5.7 as the half-life. So apparently I have correctly figured out what you are supposed to do.)
Click to expand...

Yeah, I'm sorry about that, I was a little confused myself (
 
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