Suppose that the equation represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places.
A)after 3.66 years
B)after 4.30 years
C)after 100.00 years
D)after 0.22 year
E)after 1.12 years

Question

Suppose that the equation  represents the number of employees working t years after a company begins operations. After how many years will at least 300 employees be working? Round your answer to two decimal places. ​
A)after 3.66 years 
B)after 4.30 years 
C)after 100.00 years 
D)after 0.22 year 
E)after 1.12 years

Quizplus · Accepted Answer

To solve for the number of years t where at least 300 employees are working, we can set the given equation equal to 300 and solve for t.

11eb0d3b_981a_b288_9790_19d77edba153_TB1243_11 = 300

Taking the natural logarithm of both sides:

ln(11eb0d3b_981a_b288_9790_19d77edba153_TB1243_11) = ln(300)

Using a calculator, we find that ln(300) ≈ 5.70378.

Solving for t:

ln(11eb0d3b_981a_b288_9790_19d77edba153_TB1243_11) = 5.70378

t ln(1.05) = 5.70378

t = 5.70378 / ln(1.05)

t ≈ 4.30

Rounding to two decimal places, we get t ≈ 4.30 years. Therefore, the answer is B.

Suppose That the Equation Represents the Number of Employees