Answer:
C. [tex]N(t)=150\cdot 3^t[/tex]
Step-by-step explanation:
You are given the exponential function [tex]n(t)=ab^t.[/tex]
From the table, [tex]N(t)=150[/tex] at [tex]t=0,[/tex] thus
[tex]N(0)=a\cdot b^0\\ \\150=a\cdot 1\ [\text{ because }b^0=1][/tex]
Also [tex]N(t)=450[/tex] at [tex]t=1,[/tex] thus
[tex]N(1)=a\cdot b^1=a\cdot b.[/tex]
Since [tex]a=150,[/tex] substitute it into the second equation
[tex]450=150\cdot b\\ \\b=\dfrac{450}{150}\\ \\b=3[/tex]
and the expression for the exponential function is
[tex]N(t)=150\cdot 3^t[/tex]
