If there is 360 grams of radioactive material with a half-life of 8 hours, how much of the radioactive material will be left after 32 hours and is the radioactive decay modeled by a linear function or an exponential function?A. 22.5 grams; linear

B. 22.5 grams; exponential

C.45 grams; linear

D. 45 grams; exponential

Answers

Answer 1

Answer: B.) 22.5 GRAMS, EXPONENTIAL

32 hours ÷ 8 hours = 4

The radioactive material will half 4 times.

360 x (1/2)⁴ = 22.50

360 x 1/2 = 180
180 x 1/2 = 90
90 x 1/2 = 45
45 x 1/2 = 22.50

Answer 2

Answer:

Answer:

B. 22.5 grams; exponential .

Step-by-step explanation:

We have been given that there is 360 grams of radioactive material with a half-life of 8 hours.

As amount of radioactive material remains 1/2 of the amount after each 8 hours, therefore, our function will be an exponential decay function.

We will use half-life formula to solve our given problem.

$y=a*((1)/(2))^{(t)/(b)}$ , where,

$a=\text{Initial value}$ ,

$t=\text{Time}$ ,

$b=\text{Half life}$ .

Let us substitute a=360 and b=8 in half life formula to get half life function for our given radioactive material.

$y=360*((1)/(2))^{(t)/(8)}$ , where y represents remaining amount of radioactive material after t hours.

Therefore, the function $y=360*((1)/(2))^{(t)/(8)}$ gives the half-life of our given radioactive material.

Let us substitute t=32 in our half life function to find the amount of material left after 32 hours.

$y=360*((1)/(2))^{(32)/(8)}$

$y=360*((1)/(2))^(4)$

$y=360*(1^4)/(2^4)$

$y=360*(1)/(16)$

$y=22.5$

Therefore, the radioactive material will be left 22.5 grams after 32 hours and the radioactive decay is modeled by an exponential function and option B is the correct choice.

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The train at the amusement park is a scale model of a full-size train. A measure of 0.15 meter on the train at the amusement park represents 1 meter on the full-size train. The train at the amusment park is 21 meters long. What is the length of the full-size train in meters

Answers

Answer:

The length of the full-size train is 140 meters.

Step-by-step explanation:

To determine the length of the full-size train, we will use the given relationship between the train at the amusement park and the full-size train.

From the question,

0.15 meter on the train at the amusement park represents 1 meter on the full-size train,

Let the length of the full-size train be x

Now,

If 0.15 meter on the train at the amusement park represents 1 meter on the full-size train

Then, 21 meters on the train at the amusement park will represent x meters on the full-size train

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x = 21/0.15

x = 140 meters

Hence, the length of the full-size train is 140 meters.

Answer:

140m

Step-by-step explanation:

0.15 × x = 21 × 1

0.15x = 21

x = 21/0.15

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When I started here, there were 500 employees. Since then, we have added 35% more employees, so we now have a total of __________ employees.

Answers

Number of employees when i initially started = 500
Percentage increase in the number of employees = 35%
Then
Increase in the number of employees = (35/100) * 500
   = 35 * 5
   = 175
So the total number of employees = 500 + 175
   = 675
So now we have a total of 675 employees. I hope the procedure is not that complicated for you to understand. You can generally use this method for solving similar type of problems in future without requiring any help from anyone.

Samantha buys one vase and x roses. The vase costs $15 and each rose costs $2.What function equation represents the amount of money Samantha spends?

f(x)=15x−2

f(x)=2x−15

f(x)=2x+15

f(x)=15x+2

Answers

I believe the correct answer from the choices listed above is the third option. The equation that would represent the amount of money Samantha spends would be f(x)=2x+15 where 15 represents the value of the vase which is a fix amount and 2x is the value of the roses.

Hope this answers the question. Have a nice day.

Answer:

f(x)=2x+15

Step-by-step explanation:

Out of 32 students in a class, 5 said they ride their bikes to school. based on these results,how many of 800 students in the school ride threr bikes to school?

Answers

Do a proportion.
5/32= x/800
Cross multiply and divide
800 x 5= 4,000
4,000 divided by 32= 125
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Calculate the area of the circular field if its radius is 110m and express this area in hectares?

Answers

Hi There! :)

Calculate the area of the circular field if its radius is 110m and express this area in hectares?

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During a bike challenge, riders have to collect various colored ribbons. Each 1/2 mile they collect a red ribbon, each 1/8 mile they collect a green ribbon, and each 1/4 mile they collect a blue ribbon. Which colors of ribbons will be collected at the 3/4 mile marker?

Answers

Plus every fraction you will get 7/8
And the question says about the ribbons he will get at 3/4 miles

so let the whole road is 1

so, according to the equation ; (1-7/8) = 1/8

and (1-1/4) = 3/4

so the answer is green and blue

Answer:

Red ribbons: 1

Green ribbons: 6

Blue ribbons: 3

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