Exponential Functions Flashcard Review

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' in an exponential function represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.

Front

How do you determine the initial amount in an exponential function?

Back

The initial amount 'a' in an exponential function f(x) = a(b^x) is the value of the function when x = 0.

Front

If a savings account has an annual interest rate of 5%, what is the exponential function?

Back

f(x) = P(1.05)^x, where P is the initial amount.

Front

What is the formula to calculate the future value of an investment using exponential growth?

Back

Future Value = Present Value * (1 + r)^t, where r is the growth rate and t is the time in years.

Front

What is the growth rate if a population increases by 20% each year?

Back

The growth rate is 20%.

Front

How do you convert a percentage increase to a growth factor?

Back

To convert a percentage increase to a growth factor, use the formula: Growth Factor = 1 + (percentage increase / 100). For example, a 15% increase becomes 1.15.

Front

What is the population after 5 years if the current population is 100,000 and it grows at 10% per year?

Back

Population = 100,000 * (1.10)^5 = 161,051 (rounded to the nearest whole number).

Front

What does it mean if an exponential function has a base less than 1?

Back

If an exponential function has a base less than 1, it indicates exponential decay.

Front

How do you find the population after a certain number of years using an exponential function?

Back

Use the formula: Population = Initial Population * (1 + growth rate)^number of years.