I spent all my points into this so give it your best shot
2 answers:
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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:
The total cost is $95.32.
Step-by-step explanation:
Given:
Total came to $76.75. There is an 8% sales tax and 15% tip.
Now, to find the total cost.
<em>8% sales tax is there so we calculate the amount after adding sales tax:</em>
$76.75 + 8% of $76.75
The cost after sales tax is $82.89.
Now, <em>the cost after 15% tip:</em>
$82.89 + 15% of $82.89
The cost after the tip is $95.32.
Therefore, the total cost is $95.32.