Suppose the number of new homes built ,H, in a city over a period of time , t, is graphed on a retangular coordinate system where time is on a horizontal axis. Suppose that the number of new homes built can be modeled by an exponential funtion, H=p*a^t where p is the number of new homes built in the first year recorded. If you weer a homebuilder looking for work would you prefer that the value of a to be between 0 and 1 or larger than 1

If you are a homebuilder, if would you want more or less homes built each year. Gedunke.

As a homebuilder looking for work, you would prefer the value of "a" to be larger than 1 in the exponential function H = p * a^t. Let me explain why.

In this exponential function, "a" represents the growth factor or rate at which the number of new homes built increases over time. When "a" is larger than 1, it indicates exponential growth. This means that the number of new homes built will multiply and increase rapidly as time progresses.

As a homebuilder, exponential growth is advantageous because it suggests a high demand for new homes in the city. More new homes being built means there is a greater need for builders and more job opportunities in the industry. With a larger value of "a," the growth rate is faster, indicating a potentially steady stream of work for you as a homebuilder.

On the other hand, if the value of "a" is between 0 and 1 (excluding 0), it represents exponential decay. In this case, the number of new homes built will decrease over time. As a homebuilder, this scenario would imply a declining demand for new homes, which could result in fewer job opportunities.

Therefore, as a homebuilder looking for work, you would prefer a value of "a" larger than 1 in order to benefit from exponential growth and maximize job prospects.