Simplify: -0.8b+4.1c-(-3.2b)-0.1c
1 answer:
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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
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;
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:
<h2>Answer:</h2>
-1/3x
<h2>Step-by-step explanation:</h2><h3>Known :</h3>- x1 = -3
- x2 = 0
- y1 = 1
- y2 = 0
- Correct line equation
We can find the straight line equation using this formula,
Insert all we know inside the formula,
Use cross multiplication,
3(y - 1) = -1(x + 3)\
3y - 3 = -x - 3
3y = -x - 3 + 3
3y = -x
y = -1/3x
<h3>Conclusion :</h3>The correct equation is y = -1/3x