Review of all things exponential

Match the equation for each graph. You may use Desmos or a graphing calculator to assist you.

• y = 4 · 2^x

• y = (1/3) · 4^x

• y = 3 · 2^x

• y = 2 · 3^x

Match the equation for each graph. You may use Desmos or a graphing calculator to assist you.

• y = 3 · 2^x

• y = 4 · 2^x

• y = (1/3) · 6^x

• y = 6 · (1/3)^x

Answer explanation

The graph of y = 4 · 2^x shows exponential growth starting at 4 when x=0. This matches the characteristics of the correct choice, while the other options either start at different values or exhibit different growth behaviors.

Match the equation for each graph. You may use Desmos or a graphing calculator to assist you.

• y = 3 · (1/2)^x

• y = 4 · (1/2)^x

• y = (1/4) · (1/4)^x

• y = 2 · (1/2)^x

Answer explanation

The graph of y = 2 · (1/2)^x shows a decay starting at 2, which matches the correct choice. Other options either start at different values or have different decay rates.

Match the equation for each graph. You may use Desmos or a graphing calculator to assist you.

• y = (1/2) · 5^x

• y = 3 · (1/2)^x

• y = (1/4) · (1/4)^x

• y = 5 · (1/2)^x

Answer explanation

The graph of y = (1/4) · (1/4)^x shows exponential decay starting from a positive value, consistent with the characteristics of this equation. The other options do not match the graph's behavior.

Identify the equation that matches the graph.

• y = (1/3) * 4^x + 1

• y = 5 * (1/4)^x + 2

• y = 2 * 2^x - 1

• y = (1/4) * 5^x + 2

Answer explanation

The graph shows exponential growth starting from a negative value, which aligns with y = 2 * 2^x - 1. This equation indicates a vertical shift downwards, matching the graph's behavior.

Identify the equation that matches the graph.

• y = 5 * 2^(x+1)

• y = 5 * 2^(x-1)

• y = 5 * 2^x + 1

• y = 5 * 2^x - 1

Answer explanation

The correct equation is y = 5 * 2^x + 1 because it represents an exponential function that shifts the graph upward by 1 unit, matching the observed graph behavior.

Identify the equation that matches the graph.

• y = (1/2) * (1/5)^x - 1

• y = (1/2) * (1/5)^(x-1)

• y = 3 * (1/2)^x - 1

• y = (1/3) * (1/2)^(x-1) - 2

Answer explanation

The correct equation, y = (1/3) * (1/2)^(x-1) - 2, matches the graph's characteristics, showing a decay pattern with a vertical shift downwards, consistent with the graph's behavior.

Identify the equation that matches the graph.

• y = 5 * (1/2)^x + 1

• y = 4 * (1/2)^x + 2

• y = 5 * (1/2)^(x+1)

• y = (1/2) * 4^x + 2

Answer explanation

The correct equation is y = 4 * (1/2)^x + 2, as it shows a vertical shift of 2 and a decay factor of 1/2, matching the graph's behavior. The other options either have different coefficients or shifts.

Rentals in a high rise apartment building get more expensive higher up, since the views get better. The ground floor (floor 0) rent is $1,950.00. The rent increases 3% per floor. What is the rent on the 18th floor? (Express answer to the nearest penny)

Mathematical Equivalence

ON

A country pledges to reduce its annual CO₂ emissions by 2% per year. If the emissions in 2022 are 7,630 Mt (metric megatons), what are the maximum allowable emissions in the year 2040? (Express answer to the nearest whole number)

Mathematical Equivalence

ON