Which of the following situations would best be modeled by a discrete relationship? a. a teacher counts the number of students in a classroom. b. a doctor records the age of a patient and his weight every 6 months. c. max is saving for a new game. he has $10 and saves $5 each week. d. both a and c. e. all of the above.

Option d is correct.

Step-by-step explanation:

Discrete values are those which take an integer value not in fraction.

Option A is discrete because there will be certain number of students in class say 20 or 30

We can not have 20.5 students

Therefore, option a is correct.

Option B is not discrete because many people can have age say 65 and a half years and weight can be in decimals say 50.5 kgs.

Option C is correct because he is saving a proper integer number of money.

Therefore, option d is correct that is both A and C are correct.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

y=mx+