1. 08:43

from Jonathan Klos Added 0 0 0

In this video, we learn how to find any term in a geometric sequence if we are just given the first few terms. Our first step is to find the common ratio. Then, we look at some patterns of finding consecutive terms and see that we can represent repeatedly multiplying the common ratio by using an exponent. Going through some examples then, we see that we can find the 100th term by take the common ratio, and taking it to the 99th power, and then multiplying that by the first term.

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• 03:39

from Jonathan Klos Added 0 0 0

In this video, we take the first few terms of a geometric sequence, and practice finding the common ratio so that we can find the next consecutive term. To find the common ratio, we divide consecutive terms together. In this example, the common ratio is a decimal, and so we can easily multiply it to get as many terms as we want.

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• 09:08

from Jonathan Klos Added 0 0 0

In this video, we look at exponential functions and graphs and see how to shift them horizontally right or left. We play around with a table of values and changing the function around. To really understand, we then use the Desmos graphing calculator to create an exponential function with a value h subtracting from the exponent. There is a slider for the value, h, so we can easily change the values and see how it changes the graph of the function.

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• 06:17

from Jonathan Klos Added 0 0 0

In this video, we look at exponential functions and graphs, and see how to shift the graph up and down vertically. We first play around with a function and table of values to see what happens when we add a constant value to the end of a function. We then use the Desmos graphing calculator to create an exponential function with a slider where we can input different values for k, and see how changing the function results in a vertical shift of its graph.

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• 12:07

from Jonathan Klos Added 0 0 0

In this video, we look at graphs of exponential functions. We look one function that is increasing, and another function that is decreasing and compare the growth of both. We use the function to create a table of values that we can then graph the points. Since this is an exponential function, we graph a smooth curve through the points to represent all the possible points that are solutions to the function. Exponential functions are different from linear functions in that they are curved and grow or decrease really fast.

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• 07:18

from Jonathan Klos Added 0 0 0

In this video, we go a step further with looking at exponential functions and graphs, and talk about the end behavior of the functions. We look at two different graphs, and talk about what is happening as the graph is increasing or decreasing along x. We see that exponential graphs grow increasingly large without bound. They also get really close to zero, as we go the other direction. To help understand what the graphs are doing, we use the function, and think about multiplying and dividing to understand the end behavior.

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• 06:54

from Jonathan Klos Added 0 0 0

In this video, we begin looking at number patterns where we repeatedly multiply by the same number. We call these number patterns geometric sequences. A geometric sequence always has a starting value for the first term, and then each term after that is multiplied by a number we call the common ratio. To help understand geometric sequences, we compare them as well to arithmetic sequences and number patterns that grow by adding the same number repeatedly.

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• 00:05

from Tomasz Pelczar Added 0 0 0

Flowers, food, computers, students affiliations, international guests, MIT, logic, technical science, outstanding gardens and sometimes even fresh animals within local forrest ... Our polish "MIT" ...

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• 14:18

from izzit.org Added 7 0 0