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cestrela7 [59]
2 years ago
10

Find the equation of the exponential function represented by the table below: above^^^^

Mathematics
1 answer:
Nikitich [7]2 years ago
4 0

Answer:

Step-by-step explanation:

We will use 2 coordinates from the table along with the standard form for an exponential function to write the equation that models that data. The standard form for an exponential function is

y=a(b)^x where x and y are coordinates from the table, a is the initial value, and b is the growth/decay rate. I will use the first 2 coordinates from the table: (0, 3) and (1, 1.5)

Solving first for a:

3=a(b)^0. Sine anything in the world raised to a power of 0 is 1, we can determine that

a = 3. Using that value along with the x and y from the second coordinate I chose, I can then solve for b:

1.5=3(b)^1. Since b to the first is just b:

1.5 = 3b so

b = .5

Filling in our model:

y=3(\frac{1}{2})^x

Since the value for b is greater than 0 but less than 1 (in other words a fraction smaller than 1), this table represents a decay function.

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<h3><u>Answer:</u></h3>

\boxed{\boxed{\pink{\sf \leadsto Hence \ the \ area \ of \ shaded \ region \ is 264 cm^2}}}

<h3><u>Step-by-step explanation:</u></h3>

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From the figure it's clear that the area of shaded region will be the difference of areas of two circles.

Let the,

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\bf \implies Area_{Shaded}= Area_{bigger}-Area_{smaller} \\\\\bf\implies Area_{Shaded} = \pi R^2 - \pi r^2  \\\\\bf\implies Area_{shaded} = \pi ( R^2-r^2)  \\\\\bf\implies Area_{shaded} = \pi [ (10cm)^2 - (4cm)^2]  \\\\\bf\implies Area_{shaded}  = \pi [ 100cm^2-16cm^2]  \\\\\bf\implies Area_{shaded}  = \pi \times 84cm^2  \\\\\bf\implies Area_{shaded}  = \dfrac{22}{7}\times 84cm^2  \\\\\bf\implies \boxed{\red{\bf Area_{shaded} = 264 cm^2 }}

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2 years ago
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