Common 10 #4 Retake

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a(b)^x, where 'a' is the initial value, 'b' is the growth (b > 1) or decay (0 < b < 1) factor, and 'x' is the exponent.

Front

How do you determine the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, but for specific parts of the graph, it may be restricted to x > a, where 'a' is a specific value.

Front

What does the base of an exponential function represent in a growth scenario?

Back

In a growth scenario, the base of an exponential function represents the growth factor, indicating how much the quantity increases for each unit increase in x.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A(n) = P(1 + r)^n, where A(n) is the amount after n years, P is the principal amount, r is the interest rate, and n is the number of years.

Front

How do you model exponential decay?

Back

Exponential decay can be modeled using the function f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the significance of the initial value in an exponential function?

Back

The initial value in an exponential function represents the starting amount before any growth or decay occurs.

Front

How can you identify an exponential growth function from a table of values?

Back

An exponential growth function can be identified by a constant ratio of successive values, indicating that each value is multiplied by a consistent growth factor.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases over time, while exponential decay occurs when a quantity decreases over time.

Front

What does the term 'compound interest' mean?

Back

Compound interest refers to the interest calculated on the initial principal and also on the accumulated interest from previous periods.

Front

How do you find the exponential equation from a set of data points?

Back

To find the exponential equation from a set of data points, you can use regression analysis or curve fitting techniques to determine the best-fitting parameters for the equation.