Answer:
Study 1 Answers:
1) 0.76 represents the multiplier of the bacteria, in this case it is decreasing by 24% because the formula for exponential decay is 1 - r.
2) 1290 represents the initial value, or before the study began.
Study 2 Answers:
1) 1180 is the initial value, or before the study began.
2) Study 1 started with more bacteria
3) Study 1 is experiencing exponential decay, while study 2 is experiencing exponential growth
Step-by-step explanation:
Exponential functions are in the form 
, where a is the initial value, b is the multiplier, and x represents inputs, such as hours after a bacteria study.
Any multiplier above 1.00 is experiencing exponential growth, meaning it grows gradually over time, and any multiplier below 1.00 is experiencing exponential decay, meaning it decreases in population over time.
The general form for a line through two points (a,b) and (c,d) is
(c-a)(y-b)=(d-b)(x-a)
This is better than the slope forms because it works in the no slope case, as does the standard form.
If you haven't seen it before, it works because when (x,y)=(a,b) we get (c-a)(b-b)=(d-b)(a-a), both sides zero, and when (x,y)=(c,d) we get (c-a)(d-b)=(d-b)(c-a), clearly equal sides.
Here we have
(0 - -5)(y - 0) = (-9 - 0)(x - - 5)
5y = -9(x+5)
5y = -9x - 45
9x + 5y = -45
Ironically there are two standards for standard form; one with the constant alone on the right and one with the whole thing equal to zero. I like the constant alone.
Answer: 9x + 5y = -45
Check:
We check each point is on the line
(-5,0)
9(-5) + 5(0) = -45, good
(0, -9)
9(0) + 5(-9) = -45, good again
Answer: Terry should buy the half-liter of water that costs $2.11 because buying 200 litres here is cheaper.
Step-by-step explanation:
Terry is buying water and needs 22 liters. A half-liter of water costs $2.11. Using this information, 22 litres will cost:
= 22 ÷ 1/2 × 2.11
= 22 × 2 × 2.11
= $92.84
Also, A 200 -milliliter container of water costs $1.01. Using this information, 22 litres will cost:
= 22 × 1.01 ÷ 200/1000
= 22 × 1.01 × 1000/200
= 22 × 1.01 × 5
= $111.1
Based on this information, Terry should buy the half-liter of water that costs $2.11 because buying 200 litres here is cheaper.
