A could math questions

[Guest]

I don't get how to finish this question, I have started it.

2^(x+3) + 2^x = 288
2^x(2^3) + 2^x = 288
2^x(2^3+1) = 288
2^x(9)=288

and then what do I do to find 'x'?


This question below I didn't get at all. COuld you show me the steps towars the answer?

Cobalt-60, which is used extensively in medical radiology, has a half life of 5.3 years. This means that if you start with 100g of cobalt-60, in 5.3 years there will be 50 g left. After another 5.3 years, there will be 25g left, and so on. The amount left, AL, at any given time is given by the equation Al=A0 (1/2) ^ t/5.3, where A0 is the intial amount and t is the time in years. What fraction of the initial amount will be left after 15.9 years?

I got this only: AL=A0 (1/2) ^ (t/5.3)

= A0= 1/2)^(15.9/5.3)
What do you do next?

Thanks for the help,
-Anna

 

[pka]

If 2^x(9)=288 then 2^x=32. So what is x?

 

[Matt]

Hi Anna,

I don't get how to finish this question, I have started it.

2^(x+3) + 2^x = 288
2^x(2^3) + 2^x = 288
2^x(2^3+1) = 288
2^x(9)=288

and then what do I do to find 'x'?

Like pka wrote, divide both sides of the last equation by 9 (in order to isolate the terms that contain x):

. . . . 2^x = 32

and now, you might notice that

. . . . 32 = 2⁵

which makes the equation

. . . . 2^x = 2⁵

and now we can read off the solution: x = 5.

 

[dagr8est]

Cobalt-60, which is used extensively in medical radiology, has a half life of 5.3 years. This means that if you start with 100g of cobalt-60, in 5.3 years there will be 50 g left. After another 5.3 years, there will be 25g left, and so on. The amount left, AL, at any given time is given by the equation Al=A0 (1/2) ^ t/5.3, where A0 is the intial amount and t is the time in years. What fraction of the initial amount will be left after 15.9 years?

You're in luck because I just learned this in physics. It's kind of hard to use scientific variables on the computer without making a mess so I'll just use:

After=Before(1/2)^(total time/half-life)
After=100(1/2)^(15.9/5.3)
After=100(1/2)^3
After=100(1/8)
After=12.5g

It's asking for the fraction of the original so:

12.5/100=1/8

So 1/8 of the original is left over.