Which of these preserve orientation- dilation, translation, reflection, and rotation.
1 answer:
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Answer:
- P(t) = 100·2.3^t
- 529 after 2 hours
- 441 per hour, rate of growth at 2 hours
- 5.5 hours to reach 10,000
Step-by-step explanation:
It often works well to write an exponential expression as ...
value = (initial value)×(growth factor)^(t/(growth period))
(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...
P(t) = 100·2.3^t
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(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours
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(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t
P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour
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(d) We want to find t such that ...
P(t) = 10000
100·2.3^t = 10000 . . . substitute for P(t)
2.3^t = 100 . . . . . . . . divide by 100
t·log(2.3) = log(100)
t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000
Answer: or
Step-by-step explanation:
The complete exercise is: "A chicken salad recipe calls for pound of chicken per serving . How many pounds of chicken are needed to make
serving".
You can convert the Mixed number to a Decimal number. Divide the numerator 1 by the denominator 2 and then add the quotient to the Whole number. Then, you get:
Now divide the numerator 1 by the denominator 8 to write the fraction to a Decimal number. Then:
Let be "x" the amount of pounds are needed to make serving.
Then, you can set up the following proportion:
Solving for "x", you get:
or