Answer:
The correct option is (C).
Step-by-step explanation:
The exponential function representing decay is as follows:
Here,
<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."
Thus, the correct option is (C).
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
2. The rate of growth of the fish from the exponential function is given as follows;
The growth factor = 1.05
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;
5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹
f(11) = 200 × (1.05)¹¹ ≈ 342
Learn more about exponential function here:
