A function is given.<br>f(x) = 2^x + 3<br>What is the value of f(-2)?

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

Andrews [41]

Answer:

The approximate difference in the half-lives of the isotopes is 66 days.

Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

$\frac{dm}{dt} = -\frac{t}{\tau}$

Where:

$m$ - Current mass of the isotope, measured in kilograms.

$t$ - Time, measured in days.

$\tau$ - Time constant, measured in days.

The solution of the differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $m_{o}$ is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

$\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}$

$\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }$

The half-life of a isotope ( $t_{1/2}$ ) as a function of time constant is:

$t_{1/2} = \tau \cdot \ln2$

$t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2$

The half-life difference between isotope B and isotope A is:

$\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|$

If $\frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9$ , $t_{A} = 33\,days$ and $t_{B} = 43\,days$ , the difference in the half-lives of the isotopes is:

$\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|$

$\Delta t_{1/2} \approx 65.788\,days$

The approximate difference in the half-lives of the isotopes is 66 days.

4 0

3 years ago

Read 2 more answers

A floor 10m by 40m is covered by square tiles 20cm. How many tiles are needed to cover the floor?

Lady_Fox [76]

Answer:

10,000

Step-by-step explanation:

We can find the area of the floor in cm^2 and divide by the are of 1 tile in cm^2.

1 m = 100 cm

10 m = 1000 cm

40 m = 4000 cm

area of floor = LW = 1000 cm * 4000 cm = 4,000,000 cm^2

area of tile = s^2 = (20 cm)^2 = 400 cm^2

number of tiles = 4,000,000/400 = 10,000

Answer: 10,000 tiles

4 0

3 years ago

An owner of a small store knows that in the last week 54 customers paid with cash, 42 paid with a debit card, and 153 paid with

djverab [1.8K]

<u></u>You would add 54+42+153=249 to find the total amount of customers from the previous week. Then you would divide 54/249= 0.2168 to find the amount of customers that used cash to total customers. The closest fraction would be about 1/5.

6 0

3 years ago

Read 2 more answers

You order two tacos and a salad. The salad costs $3.00, and you leave a $2 tip. You pay a total of $8.00. How much does each tac

Schach [20]

Each taco will cost you $1.50.

5 0

2 years ago

What is the value of arc sin(2√2)?

Artyom0805 [142]

The exact value of arcsin ( 2 √ 2 ) is π4.

8 0