A big company plans to expand its franchise and, with this, its number of employees. For tax reasons it is most beneficial to expand the number of employees at a rate of 5% per year. If the company currently has 4, 730 employees, how many years will it take until the company has 6, 000 employees? Round your answer to the nearest hundredth.

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sujoy17 sujoy17

14-05-2017
Mathematics

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A big company plans to expand its franchise and, with this, its number of employees. For tax reasons it is most beneficial to expand the number of employees at a rate of 5% per year. If the company currently has 4, 730 employees, how many years will it take until the company has 6, 000 employees? Round your answer to the nearest hundredth.

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jdoe0001 jdoe0001 · Answer 1 · 2017-05-14T22:01:22+02:00

[tex]\bf A(t)=4730(1+r)^t\qquad \begin{cases} A(t)=\textit{amount of employees}\\ r=rate\\ t=years\\ ----------\\ A(t)=6000\\ r=5\%\to \frac{5}{100}\to 0.05\\ t=years \end{cases} \\\\\\ 6000=4730(1+0.05)^t\implies 6000=4730(1.05)^t\\\\\\ \cfrac{6000}{4730}=1.05^t \\\\\\ \cfrac{600}{473}=1.05^t\implies log\left( \cfrac{600}{473} \right)=log[(1.05)^t] \\\\\\ log\left( \cfrac{600}{473} \right)=t\cdot log(1.05)\implies \cfrac{log\left( \frac{600}{473} \right)}{log(1.05)}=t[/tex]