contestada

The average price of a movie ticket in 1990 was $4.25. Since then the price has increased by approximately 3.6% each year. Write an exponential function to find the price of a ticket in 2022.

Respuesta :

opudodennis

Answer:

The function is [tex]A_t=A_oe^{rt}[/tex]

A(2022)=$13.45

Step-by-step explanation:

-Let A denote the ticket price.

The general equation for an exponential function is given as:

[tex]A_t=A_oe^{rt}[/tex]

Where:

  • [tex]A_t[/tex]=is the ticket price at time t
  • [tex]t[/tex] is the time
  • [tex]A_o[/tex] is the initial ticket price
  • [tex]r[/tex] is the rate of growth.

Given the rate of growth is 3.6% per year and the initial ticket price was $4.25:

#First find the time interval:

[tex]t= t_f-t_s\\\\=2022-1990\\\\=32 \ yrs[/tex]

we substitute our parameter values to estimate the ticket price in 2022:

[tex]A_t=A_oe^{rt}\\\\=4.25e^{0.036\times 32}\\\\=13.45[/tex]

Hence, the ticket price in 2020 is $13.45

Otras preguntas