Final answer:
The exponential model with an initial value of 270 and a 7% growth rate is represented by the formula y(t) = 270 · (1.07)^t, which predicts the value after t growth periods.
Step-by-step explanation:
We need to construct an exponential model to describe the growth of a quantity over time. Given an initial value of 270 and a 7% growth rate per period, our model will take the form of y(t) = a · b^t, where a is the initial value and b is the growth factor per period. Since the growth rate is 7%, this translates to a growth factor of b being 1.07 (100% + 7%).
The exponential growth formula therefore is y(t) = 270 · (1.07)^t. This model can be used to predict the value of the quantity after t periods of growth at this rate.
The rule of 70 is a separate concept that provides an estimate of the time required to double a quantity at a given growth rate. It is not part of the exponential model itself but can be useful for understanding the implications of exponential growth.