Alg 1 Midterm Review Part 3

Front

What is the equation that models the value of a car that loses \( \frac{1}{5} \) of its value every year if it was bought for $15,000?

Back

The equation is \( y = 15000 \left( \frac{4}{5} \right)^x \) where \( y \) is the value of the car after \( x \) years.

Front

What is the most reasonable domain for the function \( y = 15000 \left( \frac{4}{5} \right)^x \)?

Back

The most reasonable domain is \( 0 < x < 20 \).

Front

What is the asymptote of the function \( y = 2^x - 3 \)?

Back

The asymptote is \( y = -3 \).

Front

How can you determine if a sequence is Arithmetic or Geometric?

Back

An Arithmetic sequence has a constant difference between terms, while a Geometric sequence has a constant ratio between terms.

Front

Identify the type of sequence: 7.3, 7, 6.7, 6.4, 6.1...

Back

This is an Arithmetic sequence.

Front

What is the model for the amount of a radioactive isotope that halves every year starting with 100 isotopes?

Back

The model is \( f(x) = 100 \left( \frac{1}{2} \right)^x \) where \( x \) is the number of years.

Front

What type of relationship is used in exponential decay?

Back

The type of relationship is a ratio.

Front

Define exponential decay in the context of a radioactive isotope.

Back

Exponential decay refers to the process where the quantity of a substance decreases at a rate proportional to its current value.

Front

What is the general form of an exponential decay function?

Back

The general form is \( f(x) = a \left( b \right)^x \) where \( 0 < b < 1 \) and \( a \) is the initial amount.

Front

What does the variable \( x \) represent in the function \( y = 15000 \left( \frac{4}{5} \right)^x \)?

Back

The variable \( x \) represents the number of years since the car was purchased.