Question

he annual average price per square foot for office space in a city was $31.32 in 2004, and it was $66.91 in 2015. Find an exponential function of the form P(t)=P₀ᵏᵗ that models the price per square foot (P) as a function of time (t).

Answer 1

To model the office space prices as an exponential function, set the initial price P₀ to $31.32, and use the 2015 price to calculate the growth rate k. Following the steps, the final equation will represent the price per square foot as a function of time.

Step-by-step explanation:

To find an exponential function that models the price per square foot (P) as a function of time (t), we need to use the given data: the price per square foot in 2004 ($31.32) and in 2015 ($66.91).

We can represent this relationship using the exponential function P(t) = P0kt, where P0 is the initial price per square foot, k is the growth rate, and t is the time in years since the base year (2004).

Step 1: Set the initial value P0 to the 2004 price, which is $31.32, so P0 = 31.32.

Step 2: Use the price from 2015 to find the growth rate k. The time between 2004 and 2015 is 11 years, so t = 11.

Step 3: Substitute P(t) = 66.91, t = 11, and P0 = 31.32 into the equation to solve for k.

Step 4: Divide both sides by P0 to isolate kt, resulting in k11 = 66.91/31.32.

Step 5: Take the 11th root of both sides to get k.

After calculating k, we can write the final exponential function for office space prices.