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gladu [14]
2 years ago
8

Write a quadratic function with zeros -1 and 5.

Mathematics
1 answer:
Shalnov [3]2 years ago
3 0

Answer:

x^2+4x-5

Step-by-step explanation:

Zeros of a quadratic equation are -1 and 5.

Sum of zeros = -1 + 5 = 4

Product of zeros = (-1)(5) = -5

The quadratic equation will be :

x^2+(\text{sum of zeros})x+\text{product of zeros}\\\\=x^2+4x-5

So, the required quadratic equation is x^2+4x-5.

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The exponential function representing decay is as follows:

y=y_{0}\cdot e^{kt};\ k

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<em>y</em> = final value  

<em>y</em>₀ = initial value  

<em>k</em> = growth rate  

<em>t</em> = time passed

The graph represents exponential decay is:

"On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2."

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2 years ago
Park rangers tagged fish in a state park to track their population. The function f(x)=200(1.05)x can be used to find the populat
Sedbober [7]

The given exponential function can be used to determine the

population of the fish at different times.

Response:

1. 200

2. 0.05

3. Please find attached the graph of the exponential function and the table

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. Range; [0, ∞)

Domain: [200, ∞)

5. 346 fishes (approximate value)

<h3>How is the population of the fish obtained from the exponential function?</h3>

The given function is f(x) = 200·(1.05)ˣ

1. The initial population is given by the value of the function when x = 0,

which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

  • The initial population of the fish is <u>200</u>

2. The rate of growth of the fish from the exponential function is given as follows;

The growth factor = 1.05

  • The growth rate =<u> 0.05</u>

3. Please find attached the graph of the exponential function created

with MS Excel.

The asymptote of the exponential function is the line, <u>y = 0</u>

The table of values is presented as follows;

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. The domain is the possible x-values which is; 0 ≤ x < ∞

The range is the possible y-values which is; 200 ≤ f(x) < ∞

Which gives;

  • Domain; [0, ∞)
  • Range: [200, ∞)

5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹

f(11) = 200 × (1.05)¹¹ ≈ 342

  • The population of the fish after 11 years is <u>346 (fishes)</u>

Learn more about exponential function here:

brainly.com/question/15662160

3 0
2 years ago
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