Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , (H = p*a^t) where p is the number of new homes built in the first year recorded, and t is the number of years. You are going to decide if you would like to be a homebuilder in this market. Step 1 is to choose a value for “p” between 50 and 100; this is the initial number of homes built. Step 2 is to choose a value for “a”; this is the growth factor – you can choose “a” to be any number between 0 and 1 “OR” choose “a” to be any number greater than 1. Do not choose 0 or 1, as these are trivial cases. 1) Insert the chosen values for “p” and “a” into the formula listed above. 2) Use the formula to find the number of homes built, H, at any three values of time, t, in years that you want. Show your calculations and put units on your final answer!

Question

Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , (H = p*a^t) where p is the number of new homes built in the first year recorded, and t is the number of years.   You are going to decide if you would like to be a homebuilder in this market.   Step 1 is to choose a value for “p” between 50 and 100; this is the initial number of homes built.   Step 2 is to choose a value for “a”; this is the growth factor – you can choose “a” to be any number between 0 and 1 “OR” choose “a” to be any number greater than 1. Do not choose 0 or 1, as these are trivial cases.   1) Insert the chosen values for “p” and “a” into the formula listed above.   2) Use the formula to find the number of homes built, H, at any three values of time, t, in years that you want. Show your calculations and put units on your final answer!

Anonymous · Answer

built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , (H = p*a^t) where p is the number of new homes built in the first year recorded, and t is the numbe

Explain Bot · Answer

To decide whether you'd like to be a homebuilder in this market, you need to choose values for "p" and "a" and use the given formula to calculate the number of homes built at different times. Here is a step-by-step guide on how to do that: Step 1: Choose a value for "p" between 50 and 100. Let's say you choose p = 75. Step 2: Choose a value for "a" either between 0 and 1 or larger than 1. For the purpose of this explanation, let's choose a = 1.5 (greater than 1). Now, let's plug in the chosen values of p and a into the given formula: H = p * a^t 1) Calculation for the first value of time, t = 1 year: H = 75 * (1.5^1) (Substitute p = 75, a = 1.5, and t = 1) H = 75 * 1.5 H = 112.5 Therefore, if you start building homes in year 1, the number of homes built would be 112.5. 2) Calculation for the second value of time, t = 3 years: H = 75 * (1.5^3) (Substitute p = 75, a = 1.5, and t = 3) H = 75 * 3.375 H = 253.125 Therefore, if you start building homes in year 3, the number of homes built would be 253.125. 3) Calculation for the third value of time, t = 5 years: H = 75 * (1.5^5) (Substitute p = 75, a = 1.5, and t = 5) H = 75 * 11.39 H = 854.25 Therefore, if you start building homes in year 5, the number of homes built would be 854.25. Keep in mind that these values are based on the chosen values of p and a. You can choose different values for p and a to see how it affects the growth of homes built over time.