Answer:
The solution is [tex]t = -52.66[/tex]
Step-by-step explanation:
The first step to solve this equation is placing everything with the exponential to one side of the equality, and everything without the exponential to the other side. So
[tex]400e^{-0.0174t} = 1000[/tex]
[tex]e^{-0.0174t} = \frac{1000}{400}[/tex]
[tex]e^{-0.0174t} = 2.5[/tex]
The ln is the interse operation to the exponential, so we apply the ln to both sides of the equality.
[tex]\ln{e^{-0.0174t}} = \ln{2.5}[/tex]
[tex]-0.0174t = 0.9163[/tex]
[tex]t = -\frac{0.9163}{0.0174}[/tex]
[tex]t = -52.66[/tex]
