Sup!
Hold on, look at this.
Stellar, right?
Exponential growth problems are all about showing how something gets bigger (or grows) over time. Think of it like watching money magically multiply in your bank account if you just leave it alone—no work required! When you see these on the SAT, you’ll likely get a word problem that involves a percent increase over time.
Let’s go through the steps, so you’ll know exactly what to do on test day and can keep that test anxiety or SAT anxiety under control.
The Formula: A = P(1 + r)^t
The key to solving these problems is understanding the formula, which looks like this:
Let’s break down what each letter means:
- A is the final amount (or how much you end up with after the growth period).
- P is the initial amount or principal (the starting value, like how much money you put in the bank at the start).
- r is the rate of growth, or the percent increase written as a decimal (so if it’s 5%, you’ll write it as 0.05).
- t is the time, usually given in years or other units.
In word problems, these exponential growth formulas often describe money, populations, or anything that’s growing at a steady rate over time.
Step 1: Identify Your Variables
Let’s look at an example SAT problem to walk through how this works.
Example: Suppose you deposit $1,000 in a savings account that earns 3% interest per year. You leave it alone, and after 5 years, you want to know how much money you’ll have.
The first step is to pick out each part of the formula from the information you’re given.
- P (the starting amount) is $1,000.
- r (the growth rate) is 3%, which we’ll write as 0.03.
- t (the time) is 5 years.
Now that we have our values, let’s plug them into the formula.
Step 2: Plug In the Values
Step 3: Calculate the Final Amount
So, after 5 years, you’d have around $1,159 in the account if you just let it sit and earn interest. Not bad for doing nothing, right?
Another Example to Practice
Let’s try another example for practice.
Example: A town has a population of 10,000 people. If the population grows by 2% each year, what will the population be in 10 years?
So, after 10 years, the population would be around 12,190 people.
Tips for Reducing SAT Anxiety on Exponential Growth Problems
When SAT anxiety tries to creep in, remember that these problems are all about plugging in values and following the steps. Here are a few tips to keep calm:
- Start by identifying your values: Find the initial amount, the rate, and the time. Once you have these, you’re halfway there!
- Don’t rush the calculations: Use your calculator carefully, especially when raising numbers to a power.
- Plug and play: The formula is just a tool. Once you set it up, the math does the work for you!
If test anxiety makes you second-guess yourself, just check that you have all the values in the right place, then go for it!
Final Thoughts
Exponential growth problems don’t have to be difficult. Once you know how to use A=P(1+r)^t, it’s just about plugging in values and letting the formula work its magic. Whether you’re calculating the future value of a savings account or a growing population, the steps are the same. Remember to take it slow, follow each step, and don’t let SAT anxiety get in the way.
Keep checking back in with this blog for more tips and tricks to make SAT math less stressful and a lot more manageable. With practice and a clear approach, you’ll be ready to tackle exponential growth problems with confidence. Good luck, and go get that SAT score you deserve!