Question

The half-life of carbon-14 is approximately 6000 years. Scientists obtain 100kg. Find a formula to represent this equation.

Answer 1

It's in the form f(x) = ab^x. I think you use the two points (0,100) and (6000, 1).

Answer 2

actually in 6000 years it will be half of 100 , or 50 kg

Answer 3

so (0,100) and (6000, 50)

Answer 4

Ah, OK. Thanks.

Answer 5

Still stuck on the rest.

Answer 6

did you try to plug in values?

Answer 7

Yes. I did 50 = ab^6000. Then, a = 50/b^6000.
Then, 100 = 50/b^6000(b)^0
100 = 50/b^6000
100b^6000 = 50
b^6000 = 1/2

Answer 8

carbon-14 is approximately 6000 years. Scientists obtain 100kg. Find a formula to represent this equation.
so we want to use
y = a*b^x
we have points (0,100 ) and (6000 , 50)

first plug in (0,100) in y = a*b^x

100 = a * b^0
100 = a*1
100 = a

This gives us
y = 100 * b^x

plug in (6000 , 50)

50= 100 * b^(6000)

50/100 = b^(6000)

The left side simplifies to 1/2 or 0.5

0.5 = b^(6000)

take the power of 1/6000 to both sides


(0.5) ^(1/6000) = (b^6000)^(1/6000)

by laws of exponents the right side cancels

(0.5) ^(1/6000) = b^(6000*1/6000)

(0.5) ^(1/6000) = b^1

(0.5) ^(1/6000) = b

Therefore we have

y = 100 * (0.5 ^(1/6000)) ^ x

Now you have to options, you can evaluate 0.5 ^ (1/6000)
which is approximately 0.99988
or you can leave it and multiply by the exponent x.

option 1:

y = 100 * (0.99988)^x

option 2:

y = 100 * (0.5 ^(1/6000)) ^ x
or
y = 100 * 0.5 ^ (x/6000)