There Were 230600 Jobs Available In The Field Of Radiology In The Year 2014. Each Year, That Number Is Expected To Grow By 0.9%. Write A Function That

There were 230600 jobs available in the field of radiology in the year 2014. Each year, that number is expected to grow by 0.9%. Write a function that gives the expected number j(t) of jobs in radiology t years from the year 2014

 

Answer:

The function model that gives the expected number of jobs in radiology for a number of years from 2014 is J(t)=230,600(1+0.009t).

Further Explanation

Though Simple Interest formula, in business mathematics, deals with money problem, the same formula can also be used to different aspects which deal with similar behavior. A particular amount that is increasing as the year passes by.

The formula for simple interest is given by the equation FV = P(1+rt),

                          where FV is the future value for a specific number of years,

                                      P is the principal value or the initial value,

                                      r is the increase rate (usually in percentage), and

                                      t is the time in years

Steps in Deriving of Formula

1. t still stands for the time in years.

2. r still stands for the increase rate.

3. P still stands for the principal value.

This time we are not going to interpret the formula as a money problem but we are going to use it as a population problem.

Now substitute the values of P=230,600 and r=0.009 into the formula.

                              FV = 230,600(1+0.009t)

So the function that gives the expected number of jobs in radiology t years from the year 2014 is J(t)=230,600(1+0.009t).

Lets say for example, how many jobs available in the field of radiology in the year 2016?

This means that we are looking at 2 years after. So our time, t, is 2.

To solve the example, substitute t=2 into the function model, then simplify.

                                \begin{aligned}J(2)&=230,600(1+0.009(2))\\&=230,600(1+0.018)\\&=230,600(1.018)\\&=234,750.8\\&\approx{234,751}\end{aligned}

This means that after two years, there are approximately 234, 751 jobs available in the field of radiology from 2014.

#LearnWithBrainly

To look for a different scenarios where the simple interest formula is used, go to brainly.ph/question/2524560

To learn more about functions, click brainly.ph/question/2176209

To check some word problems about math, access the link brainly.ph/question/2198120


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