Exploring Limits of Exponential & Logarithmic Functions

• The function is discontinuous at x=a

• As x approaches a, f(x) gets arbitrarily close to L

• f(x) does not exist at x=a

What is the fundamental idea behind limits?

• Evaluating functions at a given point

• Approaching a value without necessarily reaching it

• Checking if a function is continuous

• Differentiating functions

Which of the following is an example of an exponential function in real life?

• Cooling of a hot object

• Population growth

• pH scale measurement

• Currency conversion

The Richter scale, used to measure earthquake magnitude, is based on:

• Exponential function

• Linear function

• Logarithmic function

• Quadratic function

• log a

• log x

• log e

• 1

• 1

• 0

• log p

• e

• log x

• ln e

• 1

• 0

The limit of an exponential function is useful in determining:

• How quickly a function approaches zero

• How rapidly something grows or decays

• The rate of change of straight-line motion

• The asymptotic behavior of growth models

The limit of a logarithmic function helps analyze:

• Linear equations

• Constant functions

• Slow-growing functions

• Trigonometric functions

Solve the exponential growth problem: If a population doubles every 3 years, what will be its size after 9 years if it starts at 100?

• 300

• 600

• 800

• 1000