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xxTIMURxx [149]
1 year ago
9

In 2020, there were about 260 million gas powered cars on the road. This number isexpected to decrease at a rate of 1.1% per yea

r. In 4 years, if this information iscorrect then what is the best prediction of the number of people driving gaspowered cars? Round answer to a whole number. Do not include units.
Mathematics
1 answer:
Amanda [17]1 year ago
6 0

This is an equation of exponential decay

y(t) = a b^ t where a is the initial amount

b is the decay factor

t is the time in years

b is found by taking 1 and subtracting the percent it decreases in decimal form

Letting t =4

y(t) = 260 million * ( 1- .011) ^ 4

=248.7473796 million

=24874737.96

Rounding to a whole number

= 24874738

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Let's put more details in the figure to better understand the problem:

Let's first recall the three main trigonometric functions:

\text{ Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}\text{ Tangent }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Adjacent Side}}

For x, we will be using the Cosine Function:

\text{ Cosine }\theta\text{ = }\frac{\text{ Adjacent Side}}{\text{ Hypotenuse}}Cosine(45^{\circ})\text{ = }\frac{\text{ x}}{\text{ 1}6}(16)Cosine(45^{\circ})\text{ =  x}(16)(\frac{1}{\sqrt[]{2}})\text{ = x}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = x}

Therefore, x = 8√2.

For y, we will be using the Sine Function.

\text{  Sine }\theta\text{ = }\frac{\text{ Opposite Side}}{\text{ Hypotenuse}}\text{ Sine }(45^{\circ})\text{ = }\frac{\text{ y}}{\text{ 1}6}\text{ (16)Sine }(45^{\circ})\text{ =  y}\text{ (16)(}\frac{1}{\sqrt[]{2}})\text{ = y}\text{ }\frac{16}{\sqrt[]{2}}\text{ x }\frac{\sqrt[]{2}}{\sqrt[]{2}}\text{ = }\frac{16\sqrt[]{2}}{2}\text{ 8}\sqrt[]{2}\text{ = y}

Therefore, y = 8√2.

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Thank you. please mark me the braniliest.

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Answer:

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