Solve the problem

Question

Let p be the percentage of people who are unsatisfied with their current job at t years after 1990. A reasonable model is P=0.81t+26.1. In which years will more than 50% of people be unsatisfied with their jobs.?

Answer 1

Let's assume a 50% of people unsatisfied with their jobs, then P = 50

so 50 = 0.81 * t + 26.1

t = (50 - 26.1) / 0.81 = 29.51 years

so more than 50% of people unsatisfied with their jobs means P > 50% which also means t > 29.51 years

then the first year the percentage will exceed 50% is year 30

Since t years after 1990, then the year is 2020 (1990 + 30)

Answer 2

Hi Ashley,

Here's the solution for this problem:

Since you are given the linear equation which establishes the relationship between % of people who are not satisfied p and the time t, you can easily plug p=50 into the equation and solve it for t to find the years. We will have:

50 = 0.81t +26.1

0.81t=50-26.1=23.9

t=23.9/0.81=29.5

If we round, we will get 30 years. This means that in 30 (29.5 if we don't round) years about 50% of people won't be satisfied with their jobs.

Answer 3

first we solve for p=50 so, 50=0.8t +26.1

23.9 = 0.8t

t= 29.875

but this is the number of years after 1990, so we need to add 1990 and get 2019