In Mona’s new video game she earns 30 points for each fish caught and 80 points for each octopus captured, but she loses 15 poin
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we have the function
Part a
For t=7
substitute in the given function
For t=14
For t=21
For t=28
For t=35
Observation: The values of E varies from -1 to 1, including the zero
Part B
Remember that
The Period goes from one peak to the next
so
Period=2pi/B
B=pi/14
Period=(2pi)/(pi/14)=2pi*14/pi=28
<h2>the period is 28 days</h2>We will conclude that:
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
<h3>Comparing the domains and ranges.</h3>
Let's study the two functions.
The exponential function is given by:
f(x) = A*e^x
You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:
y > 0.
For the logarithmic function we have:
g(x) = A*ln(x).
As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:
So the range of the logarithmic function is the set of all real numbers.
<h3>So what we can conclude?</h3>- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
If you want to learn more about domains and ranges, you can read:
