Exponential relations: equations, tables and graphs

Complete the table for y = 2^x when x = 0, 1, 2, 3 and 4.

What feature of a table suggests an exponential relation rather than a linear relation?

State the initial value of y = 5(1.2)^x.

State the growth factor in y = 3(2)^x.

State whether y = 100(0.8)^x represents growth or decay. Explain.

Find y when x = 3 for y = 4(1.5)^x.

Explain why the graph of y = 2^x does not have a constant gradient.

What is the y-intercept of y = 7(0.9)^x?

Correct this misconception: “An exponential graph always increases.”

Give one real situation that may be modelled exponentially.

Create a table for y = 3(2)^x from x = 0 to 5, then describe the graph shape.

Compare y = 2x + 3 with y = 3(2)^x using tables. Explain how linear and exponential patterns differ.

A population starts at 800 and grows by 6% per year. Write an exponential model and predict the population after 4 years.

A car worth $28 000 depreciates by 12% each year. Write a decay equation and estimate its value after 3 years.

Explain how the values in a table, the equation and the graph all show the same exponential relationship.

Given values 6, 9, 13.5, 20.25, decide whether the pattern is exponential and find the multiplier.

Sketch the key features of y = 10(0.5)^x and describe the intercept and long-term behaviour.

A student models a fixed $50 increase each year using an exponential equation. Explain the error and suggest a better model.

Create an exponential growth or decay question, solve it and interpret the answer in context.

Write a full worked comparison of two exponential models with different initial values and growth factors.