Question

Find the percent rate of growth for an exponential function that contains the ordered pairs (0, 20) and (1, 20)

Answer 1

The exponential function representing the given ordered pairs (0, 20) and (1, 20) exhibits no growth, as the percent rate of growth is determined to be 0. Consequently, the function remains constant at a value of 20 throughout the given time period.

Step-by-step explanation:

The provided ordered pairs (0, 20) and (1, 20) describe the behavior of an exponential function. The general form of an exponential function is , where P(t) represents the function's value at time , is the initial value, is the percent rate of growth in decimal form, and is the time.

In this scenario, the initial value is given as 20, and the time increases by 1 from the first point to the second. By substituting these values into the formula, we derive two equations. The first, for the initial point (0, 20), simplifies to 20 = 20, confirming the initial value. The second equation, representing the second point (1, 20), leads to .

Solving for , we find that r = 0, indicating no growth between the two points. The function's percent rate of growth is zero, implying a constant value of 20 over the given time period. This result aligns with the observation that the function remains unchanged, reflecting a stable state rather than exponential growth or decay.

Answer 2

The exponential function representing the given ordered pairs (0, 20) and (1, 20) exhibits no growth, as the percent rate of growth
`(\( r \))` is determined to be 0. Consequently, the function remains constant at a value of 20 throughout the given time period.

Step-by-step explanation:

The provided ordered pairs (0, 20) and (1, 20) describe the behavior of an exponential function. The general form of an exponential function is
`\( P(t) = P_0 * (1 + r)^t \)`, where P(t) represents the function's value at time
`\( t \)`,
`\( P_0 \)` is the initial value,
`\( r \)` is the percent rate of growth in decimal form, and
`\( t \)` is the time.

In this scenario, the initial value
`(\( P_0 \))` is given as 20, and the time
`(\( t \))` increases by 1 from the first point to the second. By substituting these values into the formula, we derive two equations. The first, for the initial point (0, 20), simplifies to 20 = 20, confirming the initial value. The second equation, representing the second point (1, 20), leads to
`\( 20 = 20 * (1 + r)^1 \)`.

Solving for
`\( r \)`, we find that r = 0, indicating no growth between the two points. The function's percent rate of growth is zero, implying a constant value of 20 over the given time period. This result aligns with the observation that the function remains unchanged, reflecting a stable state rather than exponential growth or decay.