Exponential functions exhibit exponential growth (or decay). What does this mean to the graphs of these functions? a.. the graph
will rise or fall more dramatically than a polynomial graph. c.. the graphs represent the population of bacteria in your mouth. b.. the graph is three dimensional. d.. the exponent in the equation is less than one
2 answers:
<u>Answer:</u>
The correct option is:
Option: a
a. the graph will rise or fall more dramatically than a polynomial graph.
<u>Step-by-step explanation:</u>
The most basic exponential function is a function of the form
y=b^x
where b is a positive number.
When b>1
the function grows in a manner that is proportional to its original value. This is called exponential growth.
When 0>b>1
the function decays in a manner that is proportional to its original value. This is called exponential decay.
The graph of a exponential function increases or decreases rapidly as compared to a graph of a polynomial function.
Hence, option a is the correct answer.
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You're going to need to use Pythagoras' theorem to work this one out!
As you know, the perimeter of a triangle is just all the lengths of the sides added up.
We'll start with side AC first. We can see that A is (-8, -4) and C is (-6, -2). That means to get from A to C, we need to go 2 units to the right, and 2 units up. Which means we have our two sides to work out the length from Pythagoras' theorem. 2² + 2² = c², c = √8.
Now we'll move onto side AB. We already know A is (-8, -4) from above, and B is (-7, -8). That means to get from A to B, we have to go 4 units down, and 1 unit to the right. So once again: 4² + 1² = c², c = √17.
Lastly, we'll work out side BC. We know that B is (-7, -8) and C is (-6, -2). That means to get to C from B, we have to go 1 unit to the right and 6 units up. So, again: 1² + 6² = c², c = √37.
Now that we have all of our lengths, we simply just add them up!
√8 + √17 + √37 ≈ 13.03 units.
(I've also attached something to help you visualise how I worked it out.)
