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Hatshy [7]
3 years ago
7

For the x-values 1, 2, 3, and so on, the yvalues of a function form a geometric

Mathematics
1 answer:
Tema [17]3 years ago
4 0

Answer:

  exponential function

Step-by-step explanation:

A geometric sequence is a representation of an exponential function.

__

There are a couple of ways an exponential function can decrease in value. It can be a decaying function, or it can be a growth function that is reflected across the x-axis.

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Simplify your answer to the previous part and enter a differential equation in terms of the dependent variable xx satisfied by x
rusak2 [61]

Answer:

x'-5x=0, or x''-25x=0, or x'''-125x=0

Step-by-step explanation:

The function x(t)=e^{5t} is infinitely differentiable, so it satisfies a infinite number of differential equations. The required answer depends on your previous part, so I will describe a general procedure to obtain the equations.

Using rules of differentiation, we obtain that x'(t)=5e^{5t}=5x \text{ then }x'-5x=0. Differentiate again to obtain, x''(t)=25e^{5t}=25x=5x' \text{ then }x''-25x=0=x''-5x'. Repeating this process, x'''(t)=125e^{5t}=125x=25x' \text{ then }x'''-125x=0=x'''-25x'.

This can repeated infinitely, so it is possible to obtain a differential equation of order n. The key is to differentiate the required number of times and write the equation in terms of x.

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3 years ago
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Galina-37 [17]

Answer:

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To start you simplify everything inside parentheses.

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Then you simplify the exponents.

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Next, you simplify the multiplication signs.

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24+25

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