A group of students is discussing situations that can be modeled by exponential decay. Which of the following students are correct? Select ALL that apply. Student Response

The final value is larger
than the initial value.

The final value is smaller
than the initial value.

The base is less than 1 but
greater than 0

The base is greater than 1.

340 ways

Step-by-step explanation:

Given:

Total number of oranges = 60

Number of rotten oranges = 4

Number of oranges picked = 3

Now, number of good oranges = Total number - Rotten oranges

                                                    = 60 - 4 = 56

Now, we need to pick at least two rotten oranges.

So, the possible outcomes can be as follows:

Now, number of ways of picking 'r' distinct objects from a total of 'n' objects is given  as:

Now, picking 2 rotten oranges from a total of 4 rotten oranges is:

Similarly, picking 3 rotten oranges from a total of 4 rotten oranges is:

Now, picking 1 good orange from a total of 56 good oranges is:

Picking 0 good oranges means picking no good oranges.

Therefore, the total number of ways of picking at least 2 rotten oranges is the sum of the above two possibilities and is given as:

At least 2 rotten out of 3 picked = (2 rotten and 1 good) or 3 rotten

                                                       = 6 × 56 + 4

                                                       = 336 + 4 = 340 ways

Therefore, there are 340 ways of picking at least 2 rotten oranges when 3 oranges are picked from a total of 60 oranges.