please help meee!!!

Question

number of half lives- 0,1,2,3,4,5,6

remaining amount of substance (grams)

4000, 2000, 1000, 500, 250, 125, 62.5

(imagine all of that in a chart)

which equation best fits the data in the given table?

a. f(x)= 1/2(4,000)^x

b. f(x)= 4,000(2)^x

c. f(x)= 4,000(1/2)^x

d. f(x)=2,000(1/2)^x

Answer 1

Hello, Christina,

You can try each formula to see which one matches the data from the table. First, let's take a quick look at the possible answers and see if there are any nthat don 't make sense.

a. f(x)= 1/2(4,000)^x

1. if we consider the initial point, where x = 0, we see that this equation would quickly devolve in f(o) = 1/2, since 4000⁰ is equal to 1. As x increases, the value increases dramatically, not what we would expect for a radioactive element that is falling apart with time. Not a possible solution.

b. f(x)= 4,000(2)^x

1. Again, we see that as x increases, the amount of substance is calculated to increase. Not a possible answer.

c. f(x)= 4,000(1/2)^x

1. This looks more hopeful. As x increases, the value (1/2)^x makes an ever decreasing number. For x = 2, 2 half lives, the remaining amount is calculated to be 1/4. 1/4 of 4000 is 1000, which matches the data. At x=3, 3 half lives, the factor becomes 1/8 and the remaining amount becomes 1000. If we keep going, we see the data matches the calculations. It makes sense, becaue we lose 1/2 x times.

d. f(x)=2,000(1/2)^x

1. At x=0, we get 2,000 grams. We know that at x=0 we should have 4000, so this doesn't look good. We only go down from 2.000 in a similar fashion as the above equation, so none of the points will match the data.

I hope this helps,

Bob