Exponential Function 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.

Front

What does it mean for a quantity to double?

Back

Doubling means that the quantity becomes twice as much as it was before.

Front

If you start with $10 and it doubles every month, how much will you have after 5 months?

Back

$320

Front

What is compound interest?

Back

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Front

How do you calculate compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What is the y-intercept of a function?

Back

The y-intercept is the value of y when x is 0 in a function, representing where the graph of the function crosses the y-axis.

Front

What is the growth rate in the function f(x) = 2(1.45)^x?

Back

The growth rate is 45%.

Front

What does it mean for a function to have a base greater than 1?

Back

If a function has a base greater than 1, it indicates exponential growth, meaning the function's value increases rapidly as x increases.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'e' is the base of the natural logarithm, 'k' is the growth constant, and 't' is time.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current amount, leading to faster increases over time.