Exponentials and Logarithms 6.1-3

Front

What is the formula for exponential decay?

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the rate of decay, and 'x' is time.

Front

What is the formula for exponential growth?

Back

y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the rate of growth, and 'x' is time.

Front

What does the base of an exponential function represent?

Back

The base indicates the growth or decay factor. If the base is greater than 1, it represents growth; if between 0 and 1, it represents decay.

Front

How do you convert an exponential equation to logarithmic form?

Back

If y = a^x, then log_a(y) = x.

Front

What is the value of log_10(10)?

Back

1, because 10^1 = 10.

Front

What is the value of log_5(5)?

Back

1, because 5^1 = 5.

Front

What is the value of log_a(a)?

Back

1, because a^1 = a.

Front

What is the value of log_a(1)?

Back

0, because a^0 = 1.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

What is the general form of an exponential function?

Back

y = ab^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.