Please answer this correctly
2 answers:
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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
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:
. 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:
. Since b to the first is just b:
1.5 = 3b so
b = .5
Filling in our model:
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.
<u><em>Answer:</em></u>
Radius of the ball is approximately 6.5 cm to the nearest tenth
<u><em>Explanation:</em></u>
The ball has the shape of a sphere
<u>Surface area of a sphere can be calculated using the following rule:</u>
Surface area of sphere = 4πr² square units
<u>In the given problem, we have:</u>
Surface area of the ball = 531 cm²
<u>Substitute with the area in the above equation and solve for the radius as follows:</u>
which is approximately 6.5 cm to the nearest tenth
Hope this helps :)