The population of the bacteria after 7 hours is 230 bacteria.
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of bacteria after x hours.
Given that he starts his experiment with 200 bacteria, hence
a = 200
The bacteria grow at a rate of 2% per hour, hence:
b = 100% + 2% = 1.02
The exponential equation becomes:
y = 200(1.02)ˣ
After 7 hours:
y = 200(1.02)⁷ = 230
The population of the bacteria after 7 hours is 230 bacteria.
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I will only be writing the reasons for each and you can respond if you need clarification for anything:
1. given
2. opposite sides of a parallelogram are congruent (and a rectangle is a parallelogram so the properties apply)
3. def rectangle
4. SAS (side angle side congruence theorem)
5. CPCTC (congruent parts of congruent triangles are congruent)
1 cup and 2/4 is what she meeds to make 1 batch
The only way you can find x here is to use a trig ratio. We have the reference angle of 75, CA is 10 which is the side adjacent to the reference angle, and we are looking for the hypotenuse. The ratio that relates the side adjacent to a reference angle to the hypotenuse is cosine. Therefore,
. Solving for x we get
. Do that on your calculator and find that the hypotenuse is 38.6 m long, last choice from above.
Factor out the GCF
15x^2+20x
15x^2/5x= 3x
20x/5x= 4
Final answer: 5x(3x+4)
