Find the 9th term of the geometric sequence 5, -25, 125, ...
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<h3><u>Required</u><u> Answer</u><u>:</u><u>-</u></h3>
Here the height and length are the sides of the rectangular wall and we have to find the area.
Area of rectangle is given by:
where l is the length and b is the breadth/width according to the question. Plugging the given values:
The area of the wall is <u>1</u><u>0</u><u>5</u><u>6</u><u>0</u><u> </u><u>inch²</u>
The expression y = 4.998 · is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).
Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:
Where:
- A - y-Intercept of the exponential function.
- B - Growth factor
- x - Independent variable.
- y - Dependent variable.
Which is equivalent to the following logarithmic expression:
㏑ y = ㏑ A + B · x
If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:
㏑ (5 / 3) = ㏑ A - B
㏑ 135 = ln A + 3 · B
Then, we solve the system by numerical methods:
㏑ A = 1.609 (A = 4.998), B = 1.098
And the exponential function is equal to y = 4.998 · .
To learn more on exponential functions: brainly.com/question/11487261
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Given:
The two functions are:
To find:
The value of .
Solution:
We have,
We know that,
Putting , we get
Therefore, the value of is 2401.