Q2: Pre-AP Alg2 Review Questions for Retake Flashcard#1 U1L1.4-L1.5

Front

What is the general form of an exponential regression equation?

Back

Y = a(b)^x, where 'a' is the initial value and 'b' is the growth/decay factor.

Front

How can you determine if a function represents exponential growth or decay?

Back

If the base 'b' in the equation Y = a(b)^x is greater than 1, it represents growth; if 'b' is between 0 and 1, it represents decay.

Front

What is the exponential model for radioactive decay?

Back

y = a(b)^x, where 'a' is the initial amount and 'b' is the decay factor.

Front

How do you simplify the expression \( \frac{x^{-7}}{x^4} \)?

Back

\( \frac{1}{x^{11}} \) using the property of exponents that states \( x^{-m} = \frac{1}{x^m} \) and \( \frac{x^m}{x^n} = x^{m-n} \).

Front

In the context of compounding interest, what does 't' represent in the formula?

Back

't' represents time in years.

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the rate of growth or decay; it indicates how much the quantity changes for each unit increase in 'x'.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What is the formula for continuous exponential growth?

Back

The formula is A = Pe^(rt), where A is the amount after time t, P is the principal amount, r is the rate, and e is Euler's number.

Front

What does the term 'initial value' refer to in an exponential function?

Back

The initial value is the starting amount when x = 0, represented by 'a' in the equation Y = a(b)^x.

Front

How do you find the decay factor in a radioactive decay problem?

Back

The decay factor can be found by determining the ratio of the amount remaining after a certain time to the initial amount.