Since 2004, the amount of money spent at restaurants in a certain country has decreased at a rate of 8% each year. In 2004, about $2420 billion was spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2017? Write an exponential equation and use your equation to determine your final answer. In order to earn full credit, you need to write the equation and show your work.
after x years, the amount is
2420 * 0.92^x
2.480E9 * (1 - .08)^(2017 - 2004)
To write an exponential equation for this problem, we can use the formula for exponential decay:
A = P * (1 - r)^n
where A is the final amount, P is the initial amount, r is the rate of decrease as a decimal, and n is the number of years.
In this case, the initial amount spent at restaurants in 2004 is $2420 billion, and the rate of decrease is 8% or 0.08 as a decimal. We want to find the amount spent in 2017, which is 13 years later.
Plugging in the values into the equation, we have:
A = 2420 * (1 - 0.08)^13
Calculating this, we get:
A = 2420 * (0.92)^13
Now, we can use a calculator to find the final answer:
A ≈ $1168.61 billion
Therefore, about $1168.61 billion will be spent at restaurants in 2017.
To determine the amount of money that will be spent at restaurants in 2017, we need to use an exponential equation.
Let's denote the amount of money spent in 2004 as A and the number of years since 2004 as t. We can express the exponential equation as follows:
A = A0 * (1 - r)^t,
where A0 is the initial amount spent in 2004, r is the rate of decrease per year (as a decimal), and t is the number of years since 2004.
Given that A0 = $2420 billion and the rate of decrease is 8%, which is equivalent to 0.08, we can substitute these values into the equation:
A = 2420 * (1 - 0.08)^t.
To find the amount spent in 2017, we need to determine the value of t. Since 2017 is 13 years after 2004, we set t = 13:
A = 2420 * (1 - 0.08)^13.
Now we can calculate the value of A to find the answer.