Question

The graph of f(t) = 7•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?

Answer 1

When it was purchased (year 0) the coin was worth $7

Explanation:

we have

`f(t) = 7(2)^t`

This is a exponential function of the form

`y=a(b)^x`

where

a is the initial value

b is the base

In this problem we have

`a=\$7`

`b=2`

`b=1+r`

so

`2=1+r`

`r=1`

`r=100\%`

The y-intercept is the value of the function when the value of x is equal to zero

In this problem

The y-intercept is the value of a rare coin when the year t is equal to zero

`f(0)=7(2)^0`

`f(0)=\$7`

therefore

The meaning of y-intercept is

When it was purchased (year 0) the coin was worth $7

Answer 2

Value of the coin when it was first released

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The y-intercept is the value of f(0).

Substitute t = 0 and find the y-intercept:

• f(0) = 7 · 2⁰ = 7 · 1 = 7

This is representing the value of the coin when it was released.