In a complete sentence, write down a method you could use to determine if an equation is written in the correct way.

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

What is the difference bn Segment CD and CD?

forsale [732]

Answer:

Sometimes, the symbol – written on top of two letters is used to denote the segment. This is line segment CD (Figure 1 ). Figure 1 Line segment. It is written CD (Technically, CD refers to the points C and D and all the points between them, and CD without the refers to the distance from C to D.)

Step-by-step explanation:

Sometimes, the symbol – written on top of two letters is used to denote the segment. This is line segment CD (Figure 1 ). Figure 1 Line segment. It is written CD (Technically, CD refers to the points C and D and all the points between them, and CD without the refers to the distance from C to D.)

6 0

3 years ago

Read 2 more answers

£90 was spent on a new chair for an office. This represented 6% of the total spent on furniture. How much was spent on furniture

ad-work [718]

Answer:

£1500

Step-by-step explanation:

$\frac{100}{6} \times 90 = 1500$