Answer:
k ≈ 0.14
Step-by-step explanation:
Given
P = 300 [tex]e^{kt}[/tex]
Substitute P = 400 and t = 2 into the equation
400 = 300 [tex]e^{2k}[/tex] ( divide both sides by 400 )
[tex]e^{2k}[/tex] = [tex]\frac{4}{3}[/tex] ( take ln of both sides )
ln [tex]e^{2k}[/tex] = ln ([tex]\frac{4}{3}[/tex] )
2k = ln ([tex]\frac{4}{3}[/tex] ) ( divide both sides by 2 )
k = [tex]\frac{ln\frac{4}{3} }{2}[/tex] ≈ 0.14 ( to the nearest hundredth )
