PLEASE HELP PLEASE! questions 9 through 16!

he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost

elena-s [515]

Answer:

The bones were 12,485 years old at the time they were discovered.

Step-by-step explanation:

Amount of the element:

The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

$A(t) = A(0)e^{-kt}$

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The radioactive element carbon-14 has a half-life of 5750 years.

This means that $A(5750) = 0.5A(0)$ , and we use this to find k. So

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-5750k}$

$e^{-5750k} = 0.5$

$\ln{e^{-5750k}} = \ln{0.5}$

$-5750k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{5750}$

$k = 0.00012054733$

So

$A(t) = A(0)e^{-0.00012054733t}$

A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?

Had 100 - 77.8 = 22.2% remaining, so this is t for which:

$A(t) = 0.222A(0)$

Then

$0.222A(0) = A(0)e^{-0.00012054733t}$

$e^{-0.00012054733t} = 0.222$

$\ln{e^{-0.00012054733t}} = \ln{0.222}$

$-0.00012054733t = \ln{0.222}$

$t = -\frac{\ln{0.222}}{0.00012054733}$

$t = 12485$

The bones were 12,485 years old at the time they were discovered.

8 0

3 years ago

The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located

Katen [24]

9514 1404 393

Answer:

(h, k) = (9, -8)

Step-by-step explanation:

The function g(x) is "vertex form" for a quadratic whose vertex is (h, k). We are told the vertex is (9, -8), so we have ...

(h, k) = (9, -8) . . . . the values of h and k

7 0

3 years ago

An artist charges $980 for a portrait but gives a 5% discount. Calculate the cash price of the portrait.

Scrat [10]

Answer:

Step-by-step explanation:

1. A boutique is offering a 15% discount on a dress. Calculate the cash price for the dress if the marked price is $2300.

2. An artist charges $980 for a portrait but gives a 5% discount. Calculate the cash price of the portrait.

3. A television set has a selling price of $1950. A 10% discount is offered for cash. What amount is the cash price to the customer?

4. A store is having a sale on dining sets. The marked price is $47,320, however a discount of 12% is being offered for cash. Calculate the cash price of the dining set.

5. A tailor charges $2487 for a suit but gives a discount of 5%. What is the cash price for the suit?

6. A washing machine has a marked price of $33,000 and a discount of 6% is given for cash. What is the cash price of the washing machine?

7. Laura sees a summer dress in a store with a marked price of $1303. A discount of 9% is given on cash. What is the cash price of the summer dress?

Light behaves mainly like a wave but it can also be considered to consist of tiny packages of energy called photons. Photons carry a fixed amount of energy but have no mass. They also found that increasing the intensity of light increased the number of electrons ejected, but not their speed.

4 0

2 years ago

Round 10.054 To 2 decimal places

antoniya [11.8K]

The answer to "Round 10.054 To 2 decimal places" is 10.05

3 0

3 years ago

What is the solution of x - 9/ 7x + 2 < 0

vampirchik [111]

Answer:

x>7

Step-by-step explanation:

6 0

2 years ago