Dilation – stretching or compressing the graph of a function

Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li

krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

$A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years$

First, let us calculate the decay constant (k)

$75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036$

Next, let us calculate the half-life as follows:

$\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years$

Therefore the half-life is between 600 and 700 years

5 0

3 years ago

Help ur boy out abcdefghijklmnopqrstuvwxyz

Umnica [9.8K]

Answer:

(-6, 10)
(-10, 9)
(-11, -6)
(-5, 1)

Step-by-step explanation:

(x,y) → (x-8, y+4)

1. (2, 6)

(2-8, 6+4)

(-6, 10)

2. (-2, 5)

(-2-8, 5+4)

(-10, 9)

3. (-3, -10)

(-3-8, -10+4)

(-11, -6)

ídk man u should connect it to (11, -7) since it's the only choice closest to the right answer, but If u can write the correct then write this. there's prolly an error in that quiz ídk

4. (3, -3)

(3-8, -3+4)

(-5, 1)

 still not in the choices nanii but (5, -14) is the only choice left and also the closest, and even if u use calculator the correct answer is still (-5, 1). sigh, I hope this helper at least

5 0

3 years ago

Katrina deposited $500 into a savings account that pays 4% simple interest. How much interest will she earn in 3 years if she ma

Dovator [93]

Answer: the amount of interest after 3 years is $60

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount of money deposited.

P represents the principal or amount of money deposited.

R represents interest rate on the deposit.

T represents the duration of the deposit in years.

From the information given,

P = $500

R = 4%

T = 3 years

Therefore,

I = (500 × 4 × 3)/100

I = $60

4 0

3 years ago

Read 2 more answers

A customer would like a wall constructed that is 4 feet high. If the bricklayer wants to use all of the 1,820 bricks that he has

yan [13]

Answer: 7,280

Step-by-step explanation:

If we take the wall that is feet high and use 1,820 bricks we multiply to get the answer of 7,280. ;) Hope this helps

3 0

3 years ago

Which of these statements is true?

Bess [88]

D is the correct answer. Every square has 2 pairs of parallel sides.

8 0

3 years ago