The exponential function representing the bacteria population after t hours is f(t) = 2000 * e^(ln(0.5)/3 * t).
To find the exponential function that represents the size of the bacteria population after t hours, we can use the formula N = N0 * e^(kt), where N0 is the initial population, e is Euler's number (approximately 2.71828), k is the growth/decay constant, and t is the time in hours.
In this case, the initial population N0 is 2,000 and the population after 3 hours is 1,000. Plugging these values into the formula, we get:
N = 2000 * e^(3k) = 1000
Solving for k, we find k = ln(0.5)/3. Therefore, the exponential function representing the bacteria population after t hours is f(t) = 2000 * e^(ln(0.5)/3 * t).
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The exponential decay function representing the bacteria population after t hours is f(t) = 2000 × 0.5^(t/3), where t is the number of hours passed.
The student has observed a population of bacteria decreasing from 2,000 to 1,000 over three hours and seeks an exponential function to model the decay of the population over time, expressed as f(t). Since the population is halving every three hours, we can represent this with the function f(t) = 2000 × 0.5^(t/3), where 2000 is the initial population, 0.5 represents the halving, and t is the time in hours. The exponent (t/3) is used because the halving occurs every three hours.
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Answer:
A - amplitude
f - frequency
Q - phase
Step-by-step explanation:
A sinusoidal carrier wave can be represented as follows: f(x) = Acos(2pi*f + Q)
So to represent the original information, you can modify the following variables mentioned above. If they looking for just one variable, then use the frequency.
Answers are:
-14
10
12
42
b) sin (2x – 17°) = cos (x – 4°)
c) sin (x)= cos (x)
Show steps
Step-by-step explanation:
Use shifts to write sine and cosine in terms of each other.
a) sin (x – 5°) = cos (35°)
sin (x – 5°) = sin (90° – 35°)
sin (x – 5°) = sin (55°)
x – 5° = 55°
x = 60°
b) sin (2x – 17°) = cos (x – 4°)
sin (2x – 17°) = sin (90° – (x – 4°))
sin (2x – 17°) = sin (90° – x + 4°)
sin (2x – 17°) = sin (94° – x)
2x – 17° = 94° – x
3x = 111°
x = 37°
c) sin (x) = cos (x)
sin (x) = sin (90° – x)
x = 90° – x
2x = 90°
x = 45°
Answer:
87.5
Edited: Yea should be 56, misread it LOL.
Appoligise to that silly mistake
Step-by-step explanation: