Find the midpoint between A and C.
2 answers:
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Using an exponential equation, supposing a rate of 5%, it is found that it will take about 2.9 years for Emma's balance to reach $450.
An increasing exponential function is modeled by:
In which:
A(0) is the initial value.
r is the growth rate, as a decimal.
In this problem:
Her initial balance is of $300, hence . A(0)=300
The growth rate is of 15%, hence R =0.15
Then,
It will reach $450 after t years, for which A(t) = 450, hence:
It will take about 2.9 years for Emma's balance to reach $450
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Answer:
The second choice: graph begins in the second quadrant near the axis and increases slowly while crossing the ordered pair 3, 1. The graph then begins to increase quickly throughout the first quadrant.
Explanation:
1) As per the set of choices, the function is:
2) Therefore it is an exponential function with these characteristics:
- Since, the bases is greater than 1 (2), the function is growing in all the domain.
- The domain is all real numbers (- ∞, ∞).
- To know where the function starts, calculate the limit of f(x) as x trends to negative infinity:
That means that the range is y > 0, and so the graph starts in the second quadrant.
- You can find the y-intersection making x = 0, which is 2⁰ ⁻ ³ = 2 ⁻³ = 1/8 = 0.25. So, the graph cross the y axis at y = 0.25.
- That tells you, that the function increases slowly, at least, until that point (0, 0.25).
- The other bullet point is when x = 3: 2 ³ ⁻ ³ = 2⁰ = 1. Therefore, the graph passes through the point (3, 1).
- From that point, the function starts to increase rapidly (since it is exponential).
- Those are the characteristics given by the second choice: graph begins in the second quadrant near the x-axis and increases slowly while crossing the ordered pair 3, 1. The graph then begins to increase quickly throughout the first quadrant.
You surely will find useful to watch the graph that I have attached.
Answer:
Step-by-step explanation:
The logistic differential equation is as follows:
In this problem, we have that:
, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.
At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.
This means that when
. With this, we can find r, that is, the growth rate,
So
So the differential equation is: