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### Course: Algebra 1>Unit 8

Lesson 4: Interpreting function notation

# Function notation word problem: bank

Learn how to interpret expressions that contain a function within a real-world context. In this video, the function we interpret models an account balance over time.

## Want to join the conversation?

• Why is the initial amount defined as M(0) and not M(1)?
• no this is wrong because m=the amount of money in the account and (t) is the days and on this one it says (t) it the money from when he opened it.
• How do you determine if a function is exactly a function?
• You can use the vertical line test with graphs. Essentially, for every x-value, there should not be more than 1 y-value. When just given an equation, the f(x) notation shows that its a function. Also, if you input an x-value into the equation of a function, you should get only one answer (only one y-value).
• I'm so sorry.... I've lost sleep over this.

I believe the answer is the 1st choice, not the 3rd choice as Sal stated.

1. It would take an initial deposit of \$120,000 to make close to \$100 interest in the first month assuming 1% average annual int-rate on savings account which would be .08333% per month.
2. The function refers to the account balance after 30 days, not the interest earned (or in this case "profit"). The 3rd choice states he earned a "profit" of \$100 after 30 days which is what Sal picked.

I think it more likely that the account was very close to the opening balance of \$100 after 30 days given the pitiful interest paid. Besides, who the heck invests \$120,000 in an account with a return rate of 1% annually?

What's the error in my thinking? :-)
• The problem asks you to figure out what M(30)-M(0)=100 represents.
M(30) = the balance in the account after 30 days.
M(0) = the balance in the account after 0 days (or basically that starting balance.
Thus, M(30)-M(0) = Current balance after 30 days - Initial balance (amount invested) = 100
The 100 has to be the profit because you have subtracted the intial amount invest, the M(0).
Hope this helps.
• maybe math isnt my thing..
• Try changing the way you understand the information. I personally have a hard time listening to the videos; I just look at the diagrams. Or try to take a day off because stress isn’t the most helpful thing in the world.
• tomorrow is another day
• What happens if you don’t understand it and u watched it like 10 times.
😕
• You can try other sources...
• What is initial balance?
• Instead of calling it as initial balance, lets call that as the principal amount we invested in something.
So, M(30) is the final amount we have after thirty days.
So, when we subtracted the principal amount we invested from the final amount we had at the end of thirty days, we made \$100 dollar profit.
i.e., M(30)-M(0)=\$100

Hope it helps :)
• If f(x+2)=x^3+6x^2+12x+8, what is f(x^1/3)? could you help, please
• In this problem, we just have to work backwards. If we are given f(x + 2), all we have to do to find f(x) is substitute x with (x - 2), since that will bring us back to x from x + 2. Adding the +2 essentially moved the graph 2 units to the left, so we have to move the graph two units to the right to get f(x), which is by inputting (x - 2) for x:
f(x + 2 - 2) = (x - 2)^3 + 6 (x - 2)^2 + 12 (x - 2) + 8
f(x) = (x^3 - 6x^2 + 12x - 8) + 6 (x^2 - 4x + 4) + 12x - 24 + 8
f(x) = x^3 - 6x^2 + 6x^2 + 12x - 24x + 12x - 8 + 24 - 24 + 8
f(x) = x^3 + 0x^2 + 0x +0
As you can see, this all simplifies to just f(x) = x^3. Now we simply take the 1/3rd power of this, which is the same as taking the cube root. Taking the cube root of a simply yields the number that was cubed in the beginning. Thus:
f(x^1/3) = (x^1/3)^3
f(x^1/3) = x ^ (3/3)
f(x^1/3) = x ^ 1 = x
Hope this helps!