Which of the following exponential functions is represented by the graph? Question 15 options: A) ƒ(x) = (1∕2)x B) ƒ(x) = 2x C) ƒ(x) = −2x D) ƒ(x) = (1∕2)−x

Step-by-step explanation:

Let the equation of the exponential function is f(x) = a(b)ˣ

Two points (-2, 4) and (-1, 2) lie on the graph,

For (-2, 4),

By substituting the values in the given function,

------(1)

For second point (-1, 2),

-----(2)

Dividing equation (1) by equation (2),

b =

From equation (1),

4 = 4a

a = 1

Therefore, equation of the exponential function will be,

f(x) =

Option (A) will be the answer.

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.

answer are

step-by-step explanation: