Question

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Answer 1

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

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=(450)/(150)\\ \\b=3`

and the expression for the exponential function is

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