Question

The value of a rare painting has increased each year since it was found at a garage sale. The value of the painting is modeled by the function f(x) = 799(1.03). What
does the 799 represent? What will the painting be worth after 5 years? Round your answer to the nearest dollar.

Answer 1

799 represents the initial value of the painting

The painting will be worth $926 after 5 years to the nearest dollar

Step-by-step explanation:

The form of the exponential function is $f(x)=a(b)^{x}$ , where

• a is the initial value ⇒ (at x = 0)
• b is the growth/decay factor ⇒ (rate of change)
• If b > 1, then the function is growth ⇒ (increasing)
• If 0 < b < 1, then the function is decay ⇒ (decreasing)

The value of a rare painting has increased each year since it was

found at a garage sale

The value of the painting is modeled by the function $f(x)=799(1.03)^{x}$

We need to know what 799 represents and what the painting will

be worth after 5 years

∵ $f(x)=799(1.03)^{x}$

∵ The form of the function is $f(x)=a(b)^{x}$

- By comparing the two forms

∴ a = 799 and b = 1.03

∵ a is the initial value at x = 0

∴ 799 represents the initial value of the painting

∵ x represents the number of years

∴ x = 5

- Substitute the value of x in the function by 5

∵ $f(5)=799(1.03)^{5}$

∴ f(x) = 926.26

∴ The painting will be worth $926 after 5 years to the nearest dollar

799 represents the initial value of the painting

The painting will be worth $926 after 5 years to the nearest dollar

Learn more:

You can learn more about the functions in brainly.com/question/10382470

#LearnwithBrainly