The exponential function g, whose graph is given below, can be written as g(x)=a*b^x
2 answers:
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Answer:
A. No Solution
Step-by-step explanation:
To solve for x we would just simplify the equation so it is easier to work with. First we will combine the -7x and the -15x and when you combine then you will get -22x so the equation will look like this now we would add 22x to both sides and our equation will be
and that is not correct so the answer would be A. No solution
Answer:
Step-by-step explanation:
The <em>Richter scale</em>, the standard measure of earthquake intensity, is a <em>logarithmic scale</em>, specifically logarithmic <em>base 10</em>. This means that every time you go up 1 on the Richter scale, you get an earthquake that's 10 times as powerful (a 2.0 is 10x stronger than a 1.0, a 3.0 is 10x stronger than a 2.0, etc.).
How do we compare two earthquake's intensities then? As a measure of raw intensity, let's call a "standard earthquake" S. What's the magnitude of this earthquake? The magnitude is whatever <em>power of 10</em> S corresponds to; to write this relationship as an equation, we can say , which we can rewrite in logarithmic form as
.
We're looking for the magnitude M of an earthquake 100 times larger than S, so reflect this, we can simply replace S with 100S, giving us the equation
.
To check to see if this equation is right, let's say we have an earthquake measuring a 3.0 on the Richter scale, so . Since taking 100 times some intensity is the same as taking 10 times that intensity twice, we'd expect that more intense earthquake to be a 5.0. We can expand the equation
using the product rule for logarithms to get the equation
And using the fact that and our assumption that
, we see that
as we wanted.