Use the Distributive Property to rewrite each expression. <br> -3 (2b

Suppose an unknown radioactive substance produces 8000 counts per minute on a Geiger counter at a certain time, and only 500 cou

mariarad [96]

Answer:

The half-life of the radioactive substance is of 3.25 days.

Step-by-step explanation:

The amount of radioactive substance is proportional to the number of counts per minute:

This means that the amount is given by the following differential equation:

$\frac{dQ}{dt} = -kQ$

In which k is the decay rate.

The solution is:

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

In which Q(0) is the initial amount:

8000 counts per minute on a Geiger counter at a certain time

This means that $Q(0) = 8000$

500 counts per minute 13 days later.

This means that $Q(13) = 500$ . We use this to find k.

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

$500 = 8000e^{-13k}$

$e^{-13k} = \frac{500}{8000}$

$\ln{e^{-13k}} = \ln{\frac{500}{8000}}$

$-13k = \ln{\frac{500}{8000}}$

$k = -\frac{\ln{\frac{500}{8000}}}{13}$

$k = 0.2133$

So

$Q(t) = Q(0)e^{-0.2133t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.2133t}$

$0.5Q(0) = Q(0)e^{-0.2133t}$

$e^{-0.2133t} = 0.5$

$\ln{e^{-0.2133t}} = \ln{0.5}$

$-0.2133t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.2133}$

$t = 3.25$

The half-life of the radioactive substance is of 3.25 days.

7 0

3 years ago

The profit P in dollars, gained by selling x computers is modeled by p = -5x²+1000x+5000. How many computers must be sold to obt

olchik [2.2K]

Answer:

$p = - 5 {x}^{2} + 1000x + 5000 \\ 5500000 = - 5 {x}^{2} + 1000x + 5000 \\$

solve for x

8 0

3 years ago

Read 2 more answers

What is easy-access credit?

lana [24]

Answer:

b ) a loan given for a short period of time that is not dependent on credit history

Step-by-step explanation:

:) enjoy

3 0

3 years ago

Read 2 more answers

Select all the equations on which the point (10,0) lies.

Makovka662 [10]

Answer:

B, C

Step-by-step explanation:

Since y=0, you are looking for equations such that 10 times the coefficient of x is the constant in the equation.

a) 5·10 ≠ 15

b) 2·10 = 20 . . . . select this one

c) 10 = 10 . . . . select this one

d) 3·10 ≠ 13

e) 4·10 ≠ 20

f) 6·10 ≠ 50

8 0

2 years ago

How many solutions does the equation 3x + 6 equals -1 - 3 + 4x have?

jenyasd209 [6]

3x + 6= -1 - 3 + 4x
combine like terms

3x + 6= -4 + 4x
subtract 3x from both sides

6= -4 + x
add 4 to both sides

10= x

ANSWER: x= 10; This equation has one answer.

Hope this helps! :)

4 0

4 years ago

Use the Distributive Property to rewrite each expression. -3 (2b - 2a)