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 it is smaller than one, the function decreases.

Take a=1/2, for instance. square that, 1/4, cube it, 1/8, and so on.

As a homebuilder looking for work, you would prefer the value of "a" to be larger than 1.

Let me explain why:

In the exponential function H = p * a^t, the base "a" represents the growth rate of the number of new homes built over time. When "a" is larger than 1, it means there is exponential growth.

If "a" is between 0 and 1 (0 < a < 1), it represents exponential decay. This means that the number of new homes built would decrease over time. As a homebuilder looking for work, exponential decay would indicate a decline in job opportunities, as fewer homes are being built.

On the other hand, if "a" is larger than 1 (a > 1), it represents exponential growth. This would indicate an increasing number of new homes being built over time. As a homebuilder, exponential growth would be beneficial to you, as it suggests a growing market and more potential job opportunities.

Therefore, you would prefer the value of "a" to be larger than 1 in order to maximize your chances of finding work as a homebuilder.