Exploring Exponential Growth and Decay Models

What is required for an equation to be considered exponential?

• It must be a linear equation.

• It must include a square root.

• It must include a division by a variable.

• It must have a variable in the exponent.

What does the coefficient 'k' affect in an exponential equation?

• The y-intercept

• The horizontal asymptote

• The steepness of the curve

• The x-intercept

What role does the coefficient 'c' play in an exponential equation?

• It changes the direction of the curve.

• It shifts the graph up or down, affecting the horizontal asymptote.

• It affects the x-intercept of the graph.

• It determines the steepness of the curve.

How is the y-intercept determined in an exponential function?

• By setting x to 1 and solving for y

• By determining the slope of the curve

• By setting x to 0 and solving for y

• By finding the maximum value of the function

What happens to an exponential graph when the exponent is negative?

• The graph flips across the x-axis.

• The graph becomes linear.

• The graph flips across the y-axis.

• The graph becomes a circle.

What was the initial model used to predict COVID-19 cases in Canada?

• N(t) = 0.74e^(0.2t) + 4.5

• N(t) = 0.74e^(0.2t - 23) + 4.5

• N(t) = 0.74t^(0.2) + 4.5

• N(t) = e^(0.74t) + 4.5

How many COVID-19 cases were estimated on January 1st, 2020, using the model?

• Less than 3 cases

• Approximately 4 cases

• Exactly 4.51 cases

• More than 5 cases

What unrealistic result did the model predict for January 1st, 2021?

• 3.76 x 10^29 cases

• 0.74 cases

• 38 million cases

• 365 cases

Why are exponential models not always realistic for long-term predictions?

• They can predict more cases than the actual population.

• They always underestimate the number of cases.

• They cannot account for changes in variables.

• They are only accurate for physical phenomena.

Which of the following is NOT an application of exponential equations?

• Population growth

• Cooling of a liquid

• Radioactive decay

• Determining the area of a circle