Step $4$

We have now found that the heating formula for the metal bar is as follows.

$T=-85e^{ln(\frac{83}{85})t}100$

We are asked to solve for the time $t$ it takes for the metal bar to reach $75C.$ To do so$,$ let $T=75$ and solve for $t,$ rounding the final result to one decimal place.

$T=-85e^{ln(\frac{83}{85})t}100$

$75=-85e^{ln(\frac{83}{85})t}100$

$\frac{5}{17}=e^{ln(\frac{83}{85})t}$

$t=$

Therefore, how long $($in seconds$)$ will it take the bor to reach $75C$ under the given conditions? $($Round your answer to one decimal place.$)$

$51\mathrm{.}4,sec$