To work with functions that model real-life situations on the SAT, you need to know:
For any real number , the exponential function with base is defined as
- the definition of exponential growth and decay
Exponential growth (decay) occurs when the output of an exponential function increases (decreases) by a constant rate for a constant increase of its input.
denotes the initial value of , and the base is called the growth (decay) factor.
The relationship between the Celsius and Fahrenheit scales for temperature is given by the formula where is the temperature in degrees Fahrenheit and is the temperature in degrees Celsius. If the boiling point of curium is C, what is it in degrees Fahrenheit?
Correct Answer: D
Tip: Use a calculator.
Tip: Follow order of operations.
We're given that C. To solve for , we substitute with in the given formula.
This wrong choice is divided by , which is just one step in the calculation. In order to get the right answer, you have to multiply this by and add to the result
Tip: Just because a number appears in the question doesn’t mean it is the answer.
This wrong choice is the boiling point of curium in degrees Celsius, as stated in the prompt. We're to convert it to degrees Fahrenheit.
If you forget to add , like this
you will get this wrong answer.
This answer choice is meant to confuse you.
The magnitude of the gravitational force acting on an object of mass located a distance above Earth's surface is
where is the gravitational constant, kg is the Earth's mass and m is the Earth's radius. If the International Space Station has a mass of kg and the station operates m above the surface of the Earth, what is the gravitational force acting on it?
Correct Answer: B
We plug the given values into the equation:
If you forget to plug into the formula, you will get this wrong answer.
If you forget to account for , you will get this wrong answer.
If you forget to square the denominator, you will get this wrong answer.
If you forget , you will get this wrong answer.
- Use a calculator.
- Exponential growth: , where and
- Exponential decay: , where and
- Know the Rules of Exponents.
- Follow order of operations.
- SAT General Tips