Assignment #33 P3

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at a consistent percentage rate over time.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial amount, 'b' is the growth factor, and 'x' is the time.

Front

What does a growth factor of 1.10 indicate?

Back

A growth factor of 1.10 indicates a 10% increase in value.

Front

How do you determine the growth factor from a percentage increase?

Back

To find the growth factor from a percentage increase, convert the percentage to a decimal, add 1. For example, a 9% increase gives a growth factor of 1 + 0.09 = 1.09.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases over time, while exponential decay decreases over time, typically represented by a growth factor less than 1.

Front

What type of graph represents an exponential function?

Back

The graph of an exponential function is a curve that rises (for growth) or falls (for decay) sharply.

Front

If a function is f(x) = 200(1.50)^t, what type of growth does it represent?

Back

It represents exponential growth at a rate of 50% per time unit.

Front

What is the initial amount in the function f(x) = 100(1.10)^t?

Back

The initial amount is 100.

Front

How do you identify exponential growth from a function?

Back

Exponential growth can be identified if the base of the exponent is greater than 1.

Front

What does the term 'initial amount' refer to in an exponential function?

Back

The initial amount refers to the value of the function when time (t) is zero.