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A new popular midsize car has a retail price of $25,000. The midsize car's value M(t) is given by the exponential model M of t is equal to 25,000 times the quantity four fifths to the power of t where t represents the time in years. Identify the domain, in yearly intervals, that contains all the years the car's value is less than $1,000.
[13, ∞)
[14, ��)
[15, ∞)
[16, ∞)

Sagot :

TyeM200519

Answer:

Its C

Step-by-step explanation:

Just finished the homework and got it right

Using exponential functions, it is found that the correct option is given by:  [15, ∞)

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The exponential function given in this exercise is:

[tex]M(t) = 25000(\frac{4}{5})^t[/tex]

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The domain that contains all the years the car's value is less than $1,000 is composed by the values of t for which:

[tex]M(t) < 1000[/tex]

Thus, we have to solve the exponential inequality.

[tex]M(t) < 1000[/tex]

[tex]25000(\frac{4}{5})^t < 1000[/tex]

[tex](\frac{4}{5})^t < \frac{1}{25}[/tex]

[tex]\log{(\frac{4}{5})^t} < \log{\frac{1}{25}}[/tex]

[tex]-0.0969t < -1.39794[/tex]

[tex]0.0969t > 1.39794[/tex]

[tex]t > \frac{1.39794}{0.0969}[/tex]

[tex]t > 14.43[/tex]

Rounding, t greater than 15 years, and the correct option is:

[15, ∞)

A similar problem is given at https://brainly.com/question/16056918

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