Question

The value of a collectible toy is increasing exponentially. The two points on the graph

Answer 1

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: $y=ab^{x}$

Part A

Translating to the question, the toy's value as a function of time is

$t=ab^{w}$

To determine constants a and b, we use points given by graph.

First, (0,5) to find a:

$5=a.b^{0}$

a = 5

Now, (3,10) to determine b:

$10=5b^{3}$

$b=\sqrt[3]{2}$

b = 1.26

The toy's value as a function of time in weeks is $t=5.(1.26)^{w}$

Part B

Since, the function is in weeks:

1 week = 7 days

w weeks = 10 days

$w = \frac{10}{7}$

Replacing w:

$t=5.(1.26)^{w}$

$t=5.(1.26)^{10/7}$

Expression that represents toy's value after 10 days is $t=5.(1.26)^{10/7}$.