Advanced Functions,Exponential Functions

In summary, the current inflation rate of 2.5% is causing the cost of items to increase, including gasoline. In 2009, a liter of gasoline cost $0.90. Using the equation A=A0(1+i)^n, where A is the current cost, A0 is the initial cost, i is the inflation rate, and n is the number of years, the cost of a liter of gas in 2021 would be approximately $1.125. To find the cost of filling a 60 liter gas tank in 2021, the equation can be used again, resulting in a cost of approximately $67.50.
  • #1
ohhnana
25
0

Homework Statement


Inflation is currently causing the cost of items to increase by about 2.5% per year. In 2009 a litre of gasoline costs approximately $0.90. What will it cost to fill a 60 litre gas tank 10 years from now? Round your answer to the nearest dollar.


Homework Equations



A=A0(1+i)^n

The Attempt at a Solution


C=.90+.025*10(.90)
 
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  • #2
ohhnana said:

Homework Statement


Inflation is currently causing the cost of items to increase by about 2.5% per year. In 2009 a litre of gasoline costs approximately $0.90. What will it cost to fill a 60 litre gas tank 10 years from now? Round your answer to the nearest dollar.


Homework Equations



A=A0(1+i)^n

The Attempt at a Solution


C=.90+.025*10(.90)
= 1.125.

This answer doesn't take into account that the 2.5% increase is on the previous year's price. Use the equation you considered to be relevant to find the cost of a liter of gas in the 12 years from 2009 to 2021.

Then calculate the cost of a 60 L tank of gas.
 
  • #3
so what would A0 be?
 
  • #5
Thank You
 

1. What are advanced functions?

Advanced functions are mathematical functions that involve more complex operations and techniques than basic functions. They are often used to model real-world phenomena and are an important part of higher level mathematics.

2. How do exponential functions differ from other types of functions?

Exponential functions have a special form where the independent variable, usually denoted as x, is the exponent of a constant base. This results in a curve that increases or decreases rapidly depending on the value of the base. Other types of functions, such as linear or quadratic functions, do not have this exponential growth or decay property.

3. What are some real-world applications of exponential functions?

Exponential functions are commonly used to model population growth, radioactive decay, compound interest, and other situations where quantities increase or decrease at a rapid rate. They can also be used to describe the spread of diseases, the growth of bacteria, and the decline of natural resources.

4. How do you graph an exponential function?

To graph an exponential function, you first need to determine the value of the base and the initial value. Then, plot a few points by choosing values for the independent variable x and calculating the corresponding output. Finally, connect the points with a smooth curve to create the graph. Keep in mind that the graph of an exponential function will never cross the x-axis and will either approach positive or negative infinity as x approaches positive or negative infinity, respectively.

5. What is the inverse of an exponential function?

The inverse of an exponential function is the logarithmic function with the same base. In other words, if y = a^x is an exponential function, then its inverse is x = log_a(y). This means that the input and output of the functions are switched, and the graph of an exponential function and its inverse are reflections of each other over the line y = x.

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