Since 2005, the amount of money spent at restaurants in a certain country has increased at a rate of 6% each year. In 2005, about $490 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2014?

Question

Since 2005, the amount of money spent at restaurants in a certain country has increased at a rate of 6% each year. In 2005, about $490 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2014?

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Part 1
About $

enter your response here billion will be spent at restaurants in 2014 if the trend continues.
(Round to the nearest whole number as needed.)

Answer 1

To find out how much will be spent at restaurants in 2014, we can use the formula for compound interest: A = P(1+r)^n, where A is the final amount, P is the initial amount, r is the interest rate (in decimal form), and n is the number of years.

In this case, the initial amount is $490 billion, the interest rate is 6% (or 0.06), and the number of years is 2014 - 2005 = 9.

Substituting these values into the formula, we get:

A = $490 billion * (1 + 0.06)^9

A ≈ $490 billion * (1.06)^9

A ≈ $703.89 billion

Therefore, about $704 billion will be spent at restaurants in 2014 if the trend continues.

Answer 2

try again:

To predict the amount of money spent at restaurants in 2014, use an exponential function, y equals a times b Superscript x, where, agreater than0 and bgreater than1. The initial amount a is the number of billions of dollars spent in 2005. The base b is the growth factor, which equals 1 plus the percent rate of change expressed as a decimal. The value of x is the number of years since 2005. Check your calculations carefully.

Answer 3

To predict the amount of money spent at restaurants in 2014 using an exponential function, we can set up the equation:

y = a * b^x

where:
y = amount of money spent at restaurants in 2014
a = number of billions of dollars spent in 2005 ($490 billion)
b = growth factor (1 + rate of change expressed as a decimal) = 1 + 0.06 = 1.06
x = number of years since 2005 = 2014 - 2005 = 9

Substituting these values into the equation, we get:

y = $490 billion * (1.06)^9

y ≈ $490 billion * (1.5954)

y ≈ $781.64 billion

Therefore, about $782 billion will be spent at restaurants in 2014 if the trend continues.

Answer 4

thats inccorect correct answer: 828

Answer 5

Apologies for the incorrect response. Let's calculate it correctly.

To predict the amount of money spent at restaurants in 2014, we can use the exponential function equation:

y = a * b^x

Given:
a = $490 billion
b = 1 + 0.06 = 1.06 (growth factor)
x = 2014 - 2005 = 9 years

Substituting these values into the equation, we get:

y = $490 billion * (1.06)^9

y ≈ $828 billion

Therefore, about $828 billion will be spent at restaurants in 2014 if the trend continues.

Since 2005​, the amount of money spent at restaurants in a certain country has increased at a rate of 6​% each year. In 2005​, about ​$490 billion was spent at restaurants. If the trend​ continues, about how much will be spent at restaurants in 2014​?

To find out how much will be spent at restaurants in 2014, we can use the formula for compound interest: A = P(1+r)^n, where A is the final amount, P is the initial amount, r is the interest rate (in decimal form), and n is the number of years.

try again:

To predict the amount of money spent at restaurants in 2014 using an exponential function, we can set up the equation:

thats inccorect correct answer: 828

Apologies for the incorrect response. Let's calculate it correctly.

Since 2005, the amount of money spent at restaurants in a certain country has increased at a rate of 6% each year. In 2005, about $490 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2014?