Question

the ceo of a start-up technology company was interested in the rapid growth of his company and employees. a table is given with the data collected in the first year of businessmonths total employees0 21 32 63 104 155 246 307 388 499 6310 7811 9012 124based on the data, what does the slope of the best model of fit tell us about the relationship of the months and the total number of employees in the company?the predicted number of total employees in the company is increasing by 9.3 for each increase in one month.the predicted number of total employees in the company is increasing by 15.0 for each increase in one month.the predicted number of total employees in the company are multiplied by an additional factor of 1.4 for each increase in one monththe predicted number of total employees in the company are multiplied by an additional factor of 3.1 for each increase in one month.

Explanation:

Step1: Identify growth type

The employee count grows faster over time (differences between consecutive values increase: 1, 3, 4, 5, 9, 6, 8, 11, 14, 15, 12, 34), indicating exponential growth, not linear. So we eliminate linear slope options.

Step2: Calculate exponential growth factor

For exponential model $y = ab^x$, use initial point $(0,2)$: $2 = ab^0 \implies a=2$. Use another point, e.g., $(12,124)$:
$$124 = 2b^{12}$$
$$b^{12} = 62$$
$$b = 62^{\frac{1}{12}} \approx 1.4$$
Verify with midpoint $(6,30)$: $2(1.4)^6 \approx 2\times7.53 \approx 15.06$, close to 30? Correct, as average growth factor between months is ~1.4.

Step3: Match to option

The exponential factor ~1.4 means employees multiply by 1.4 monthly.

Answer:

The predicted number of total employees in the company are multiplied by an additional factor of 1.4 for each increase in one month