The question is incomplete. Here is the complete question.
Part A
The value of a collectible toy is increasing exponentially. The two points on the graph show the toy's initial value and its value 3 weeks afterward.
Express the toy's value t, in dollars, as a function of time w in weeks after purchase.
Part B
Write an expression to represent the toy's value 10 days after purchase
Answer and Step-by-step explanation: An exponential function is of the form: [tex]y=ab^{x}[/tex]
Part A
Translating to the question, the toy's value as a function of time is
[tex]t=ab^{w}[/tex]
To determine constants a and b, we use points given by graph.
First, (0,5) to find a:
[tex]5=a.b^{0}[/tex]
a = 5
Now, (3,10) to determine b:
[tex]10=5b^{3}[/tex]
[tex]b=\sqrt[3]{2}[/tex]
b = 1.26
The toy's value as a function of time in weeks is [tex]t=5.(1.26)^{w}[/tex]
Part B
Since, the function is in weeks:
1 week = 7 days
w weeks = 10 days
[tex]w = \frac{10}{7}[/tex]
Replacing w:
[tex]t=5.(1.26)^{w}[/tex]
[tex]t=5.(1.26)^{10/7}[/tex]
Expression that represents toy's value after 10 days is [tex]t=5.(1.26)^{10/7}[/tex].
