Given the equation:
[tex]y=4(1.8){}^t[/tex]You know that "y" represents the number of acres of land, and "t" represents the number of minutes the fire has raged.
In order to find the time (in minutes) it will take for a fire to reach 160 acres, you need to substitute this value of "y" into the equation:
[tex]y=160[/tex]And then solve for "t":
[tex]160=4(1.8){}^t[/tex]Follow these steps in order to solve for "t":
- Divide both sides of the equation by 4:
[tex]\begin{gathered} \frac{160}{4}=\frac{4(1.8){}^t}{4} \\ \\ 40=(1.8)^t \end{gathered}[/tex]- Take the logarithm from both sides:
[tex]\begin{gathered} log(40)=log(1.8)^t \\ \\ log(40)=t\cdot log(1.8) \end{gathered}[/tex]- Divide both sides by the logarithm on the right side of the equation:
[tex]\begin{gathered} \frac{log(40)}{log(1.8)})=\frac{t\cdot log(1.8)}{log(1.8)} \\ \\ t\approx6.28 \end{gathered}[/tex]Hence, the answer is:
[tex]6.28\text{ minutes \lparen approximately\rparen}[/tex]