Question

A firm starts with 90 employees, but the number of employees rises by 6% per week. How many persons will be employed in the 21st week if the present rate of expansion continues? Round up your answer to a whole number.

(a) 200
(b) 250
(c) 300
(d) 350

Answer 1

Using the formula for exponential growth, P = P0 * (1 + r)^t, the firm will have approximately 289 employees in the 21st week after rounding up. The closest answer choice is (c) 300 employees.

Step-by-step explanation:

To calculate the number of employees at the firm after 21 weeks of a 6% weekly increase, we can use the formula for exponential growth, which is P = P0 * (1 + r)^t, where P0 is the initial amount, r is the rate of increase per time period (expressed as a decimal), and t is the number of time periods.

In this case, the initial number of employees (P0) is 90, the rate of increase per week (r) is 0.06 (since 6% is equal to 0.06 when expressed as a decimal), and the number of weeks (t) is 21.

Applying these values to the formula:

P = 90 * (1 + 0.06)^21

Calculating this gives:

P ≈ 90 * (1.06)^21 ≈ 90 * 3.207 ≈ 288.63

Since we are asked to round up to the nearest whole number, the firm will have approximately 289 employees in the 21st week if the present rate of expansion continues.

The answer matches option (c) 300 when rounding up the calculated value to the nearest available option in a multiple-choice format.