Question

PLEASE HELP ASAP, I WILL GIVE BRAINLESSLY ANSWER SHOW WORK PLEASE

Answer 1

Answer:

C. $N(t)=150\cdot 3^t$

Step-by-step explanation:

You are given the exponential function $n(t)=ab^t.$

From the table, $N(t)=150$ at $t=0,$ thus

$N(0)=a\cdot b^0\\ \\150=a\cdot 1\ [\text{ because }b^0=1]$

Also $N(t)=450$ at $t=1,$ thus

$N(1)=a\cdot b^1=a\cdot b.$

Since  $a=150,$ substitute it into the second equation

$450=150\cdot b\\ \\b=\dfrac{450}{150}\\ \\b=3$

and the expression for the exponential function is

$N(t)=150\cdot 3^t$