The equation E(t) = 5(1.8)t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?
Correct answer: A. The estimated number of employees when the restaurant opened
- A. The estimated number of employees when the restaurant opened
- B. The increase in the estimated number of employees each year
- C. The number of years the restaurant has been open
- D. The percent increase in the estimated number of employees each year
Explanation
The correct answer is that the number 5 in the function E(t) = 5(1.8)t represents the estimated number of employees when the restaurant opened. In an exponential function like E(t) = a(b)t, 'a' denotes the initial value at t = 0. Thus, 5 indicates the starting number of employees. The other options are incorrect because they misinterpret the roles of the constants and variables in the exponential function. The base of the exponent, 1.8, determines the growth factor, not the initial or yearly increase in employees.
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