Three students solve a challenge math problem. every day, the number of students who solve the problem doubles. there are 384 students enrolled in the class. if the number of students who solve the problem continues to increase at this rate, how long will it take until all of the students enrolled in the class solve the problem? write an equation for the number of students who solved the problem, s= number of days since the first students solved the problem, d= the correct solution

OK, so this is assuming we are considering that the first three kids to solve ARE NOT in the first day.

So we have 3 kids and it doubles

Day 1 : 6

Day 2 : 12

Day 3 : 24

Day 4 : 48

Day 5 : 96

Day 6 : 192

Day 7: 384

So it should take 7 days or a week to solve all the problems.

The equation:

(3 * 2)^x = 384

It will take 7 days for all the class to complete the problems.

Step-by-step explanation:

We are given that 3 students solve math problems everyday.

Also, the number of students doubles each day.

So, we get the pattern,

Days (S)                             Number of students                      

1                                                     3                                                 =  3

2                                                    3 × 2                                           =  3 × 2¹  

3                                                    3 × 2 × 2                                     =  3 × 2²

4                                                    3 × 2 × 2 × 2                               =  3 × 2³

5                                                    3 × 2 × 2 × 2 × 2                         =  3 × 2⁴

6                                                    3 × 2 × 2 × 2 × 2 × 2                   =  3 × 2⁵

As, there are total 384 students in the class.

We get the equation as,

On solving, we have,

i.e.

i.e.

i.e.

i.e.

i.e.  

i.e. S = 7

Hence, it will take 7 days for all the class to complete the problems.

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer