Question

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

Answer 1

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

Answer 2

Answer:

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, $3(2)^S=384$

On solving, we have,

$3(2)^S=384$

i.e. $2^S=\frac{384}{3}$

i.e. $2^S=128$

i.e. $S\log 2=\log 128$

i.e. $S\times 0.301=2.107$

i.e. $S=\frac{2.107}{0.301}$  

i.e. S = 7

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