Answer :
We are given the function
[tex]$$
f(t) = 220(1.06)^t.
$$[/tex]
Step 1: Identify the type of function
The function is in the form
[tex]$$
f(t) = a \cdot b^t,
$$[/tex]
where [tex]$a = 220$[/tex] and [tex]$b = 1.06$[/tex]. If [tex]$b > 1$[/tex], the function represents exponential growth. Since [tex]$1.06 > 1$[/tex], the function represents exponential growth.
Step 2: Determine the starting value
The starting value is the value of the function when [tex]$t = 0$[/tex]. Calculate:
[tex]$$
f(0) = 220(1.06)^0.
$$[/tex]
Since any nonzero number raised to the power [tex]$0$[/tex] is [tex]$1$[/tex], we have:
[tex]$$
f(0) = 220(1) = 220.
$$[/tex]
Final Answer: The equation represents exponential growth, and the starting value is [tex]$220$[/tex].
[tex]$$
f(t) = 220(1.06)^t.
$$[/tex]
Step 1: Identify the type of function
The function is in the form
[tex]$$
f(t) = a \cdot b^t,
$$[/tex]
where [tex]$a = 220$[/tex] and [tex]$b = 1.06$[/tex]. If [tex]$b > 1$[/tex], the function represents exponential growth. Since [tex]$1.06 > 1$[/tex], the function represents exponential growth.
Step 2: Determine the starting value
The starting value is the value of the function when [tex]$t = 0$[/tex]. Calculate:
[tex]$$
f(0) = 220(1.06)^0.
$$[/tex]
Since any nonzero number raised to the power [tex]$0$[/tex] is [tex]$1$[/tex], we have:
[tex]$$
f(0) = 220(1) = 220.
$$[/tex]
Final Answer: The equation represents exponential growth, and the starting value is [tex]$220$[/tex].