Answer:
Every day, the mass of the sunfish is multiplied by a factor of [ln(1.34)/6].
Step-by-step explanation:
You have the following function:
[tex]M(t)=(1.34)^{\frac{t}{6}+4}[/tex]
To know what is the factor that multiplies the mass of the sunfish each day, you derivative the function M(t):
[tex]\frac{dM(t)}{dt}=(1.34)^{\frac{t}{6}+4}(\frac{1}{6})ln(1.34)\\\\\frac{dM(t)}{dt}=\frac{ln(1.34)}{6}[(1.43)^{\frac{t}{6}+4}]\\\\\frac{dM(t)}{dt}=\frac{ln(1.34)}{6}M(t)[/tex] (1)
where you have used the following general derivative:
[tex]g(t)=a^{f(t)}\\g'(t)=a^{f(t)}f'(t)ln(a)[/tex]
The derivative give you the increase in the mass per day (because t is days). By the expression (1) you can conclude that each day the mass increase a factor of [ln(1.34)/6].
Every day, the mass of the sunfish is multiplied by a factor of [ln(1.34)/6].
