A right triangle has legs of lengths 14 and 16 inches. Find the length of
1 answer:
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Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
For t=0, we have:
If we use the duplication time, we have:
Then, we have the model as:
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
The rate of growth can be calculated as dP/dt and is:
For t=8, the rate of growth is:
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as:
Solution
Problem 1:
- Kelsie pays a one-time fee for the equipment of $5.00. This is a fixed cost that never changes and is paid just once.
- Kelsie pays $18.99 for each hour (h). This means that
For 1 hour, Kelsie pays $18.99 * 1 = $18.99
For 2 hours, Kelsie pays $18.99 * 2
For 3 hours, Kelsie pays $18.99 * 3
And so on...
- We can generalize this for h hours. That is,
For h hours, Kelsie pays $18.99 * h
- Thus, Kelsie pays $18.99h after h hours separate from the initial fee of $5.00.
- Thus, her total cost would be the addition of the flat fee of $5.00 and the cost of playing for h hours. That is:
Problem 2:
- Jayson pays $35 per hour with no initial flat fee.
- Following the same logic as in the case of Kelsie, we can write the total cost incurred by Jayson after h hours is:
Final Answer
The answers are:
Problem 1:
Problem 2: