Unit 4 APPC: Exponential Functions and Series

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 a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

How do you determine the percent increase or decrease in an exponential function?

Back

To determine the percent increase or decrease, calculate the difference between the final value and the initial value, divide by the initial value, and multiply by 100.

Front

What does it mean for the rates of change of an exponential function to be proportional?

Back

It means that the rate of change of the function is directly related to the value of the function itself, leading to exponential growth or decay.

Front

How can you find the future value of an asset using exponential decay?

Back

Use the formula V = P(1 - r)^t, where V is the future value, P is the present value, r is the decay rate, and t is the time in years.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, expressed as (-∞, ∞).

Front

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

Back

The base determines the growth or decay rate of the function; if the base is greater than 1, the function represents growth, and if it is between 0 and 1, it represents decay.

Front

How do you calculate the total number of items in a stacked arrangement, such as logs?

Back

Use the formula for the sum of an arithmetic series: S_n = n/2 * (first term + last term), where n is the number of terms.

Front

What is the formula for calculating the value of a car over time using exponential decay?

Back

The formula is V(t) = V_0 * e^(-kt), where V(t) is the value at time t, V_0 is the initial value, k is the decay constant, and e is Euler's number.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the function increases over time (base > 1), while exponential decay occurs when the function decreases over time (base < 1).

Front

How do you round a number to three decimal places?

Back

To round a number to three decimal places, look at the fourth decimal place; if it is 5 or greater, round up the third decimal place by one.