If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra (all content)>Unit 11

Lesson 20: Advanced interpretation of exponential models (Algebra 2 level)

# Interpreting change in exponential models: changing units

Sal analyzes the rate of change of various exponential models for different time units by manipulating the functions that model the situations.

## Want to join the conversation?

• I noticed that about half way through the video, when the table is filled out, the initial value of 315 was written as 3.5. I suspect this was a mistake and the value Sal meant to say was 315 the whole time?
• If you are watching in fullscreen, you can exit fullscreen and see that there is a correction box at the bottom right-hand corner that lets you know he messed up. Happens all the time. EDIT: Just realized this is 7 years late...
• Given the phrasing of the question, wouldn't the answer be 1.01? I'm looking to see if this question comes up in the quiz, and if we are marked wrong because of putting in too many decimal places. Sal didn't prep very well for this one.
• Yes. If you round the answer as requested by the instructions, 1.0058 would become 1.01.
• What I did was said that if in 10 years it went up 6%, then yearly that means it goes up 0.6%, which is close to the final answer of 0.58%. Was what I did acceptable?
• No, because it's not a linear function. The error in reasoning can be seen more clearly if we use a more exaggerated example. You can't say that if in one year you get 100 percent increase (or double the original), then in 10 years you'll get 1000 percent, or 10 times as much. Try doubling a number 10 times and see the difference.
• The first value of A(t) in the table is 315, as it goes on the value becomes 3.5. Is this a mistake?
• 3.5?
Isn’t it 315?
• It is 315. The 3.5 was just a typo.
• Using this logic, can we solve compound interest problems involving fractional periods?
• Yes. You can manipulate the exponent t to however your situation is. For example, if it happens every year, you can put (t/365) for the exponent. Likewise, if it's every month, you can put (t/12) — however, be wary of how the question uses the variable.

Hopefully that helps !
• So, when I tried to model the function in terms of years instead of decades, intuitively I thought that it should look something like this:

a_years(t) = 315 * (1.06)^((1/10)t)

because in order for a_years to output an equivalent answer to a_decades, you should need to input 10 times more input into a_years. 1 year is a tenth of a decade, after all.

but Sal's model is slightly different
a_years(t) = 315 * (1.0058)^t

The first model is correct, right?
• Both models are correct, because
1.06^(0.1𝑡) = (1.06^0.1)^𝑡 ≈ 1.0058^𝑡
• Where did he get the 3.5?