There were 230,600 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 .
Do not use commas in your answer.
\[
j(t)=
\]
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Answer
Therefore, the function that gives the expected number of jobs in radiology \(t\) years from the year 2014 is \(j(t) = 230600 \cdot (1.009)^t\).
Step 1 ：The problem describes a situation of exponential growth. The general formula for exponential growth is \(j(t) = j_0 \cdot (1 + r)^t\), where \(j_0\) is the initial amount, \(r\) is the growth rate, and \(t\) is the time.
Step 2 ：In this case, \(j_0 = 230600\), \(r = 0.009\) (since 0.9% is equivalent to 0.009 in decimal form), and \(t\) is the number of years from 2014.
Step 3 ：Substituting these values into the formula, we get \(j(t) = 230600 \cdot (1 + 0.009)^t\).
Step 4 ：Therefore, the function that gives the expected number of jobs in radiology \(t\) years from the year 2014 is \(j(t) = 230600 \cdot (1.009)^t\).
