Question

The radioactive substance uranium-240 has a half-life of
14
hours. The amount
At
of a sample of uranium-240 remaining (in grams) after
t
hours is given by the following exponential function.

Answer 1

\[A(t) = 4700\left(\begin{matrix}1 \\ 2\end{matrix}\right)^{\frac{ t }{ 14 }}\]

Answer 2

Find the initial amount in the sample and the amount remaining after
60
hours.
Round your answers to the nearest gram as necessary.

Answer 3

Is that a I should know this jeez it's understandable why I need help on this jeez lol I'm a senior though

Answer 4

or*

Answer 5

yeahh lol I don't think mathway can help much until I get it started and figure out how to narrow it down to a better equation haha but thank you =)

Answer 6

@mathmate

Answer 7

Is the formula
\(A(t) = 4700\left(\begin{matrix}1 \\ 2\end{matrix}\right)^{\frac{ t }{ 14 }}\)
or is it
\(\large A(t) = 4700(\frac{1}{2})^{\frac{t}{14}}\)

Answer 8

the second one sorry

Answer 9

Use a calculator to find A(0) (initial amount, put t=0), and
A(60), i.e. put t=60 hours.

Answer 10

I'm a little confused I don't understand what I'm calculating and what it is going to answer out of the two questions =o @mathmate

Answer 11

@BloomLocke367

Answer 12

I'm not good at half-life.. sorry!

Answer 13

lol I've never even heard of it =/ but it's ok thank you anyways =)

Answer 14

@Cassandra_Lea_96
To give an example,
the quantity remaining after t=2 hours is
A(2)=4700(1/2)^(t/14)=4700(1/2)^(2/14)=4257 approximately (you'll need a calculator to calculate that).
So the answers will be similarly calculated for A(0) and A(60).

Answer 15

@mathmate can you help me out there please

Answer 16

@Cassandra_Lea_96
Have you done functions before?
Like, if f(x)=x^2+4, then f(0)=0^2+4=4, f(2)=2^2+4=8, and so on.

Answer 17

I've done functions before but this is just completely confusing me aha is the initial amount 4700? and then that times 60 is the ammount after 60 days or

Answer 18

ok so is it 240.97? it won't let me type in a fraction or anything so this is it in decimal form

Answer 19

Yes, you've got both answers correct. Decimal form is good.
Well done!