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SAT (Fall 2023)
Course: SAT (Fall 2023) > Unit 10
Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example
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Isolating quantities — Harder example
Watch Sal work through a harder Isolating quantities problem.
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At1:21, can't we just raise 1 and r to the power of t?
that would mean:
1+r^t=A/P (Since 1^anything = 1)
therefore:
r^t=(A/P) - 1
giving:
r=((A/P)-1)
Just a question. I may be wrong but I think I need some clarification here.(13 votes)
you know the formula for (a+b)^2,,,right
It contains a 2ab term
similarly ,a cubic equation contains a 3ab(a+b) term
Therefore,it's reasonable to infer that anything to the power of t would not contain isolated exponential sum of the individual terms.
Hope it helps :)(8 votes)
At 1;20, why do you need to raise t to the 1 over t power?(4 votes)
From the author:Great question! Sal is using a common method to simplify radical expressions. For example, if you have x^3 = 27, then you can take the cube root of both sides of the equation to solve for x. If you have learned about fractional exponents, remember that taking the cube root of something is the same as raising it to the (1/3) power. Similarly, taking the square root of something is the same as raising it to the (1/2) power. So, to cancel out the t power, Sal is raising both sides of the equation to the *(1/t)* power.(16 votes)
- tbh, i like this kinda isolating quantities problems. <3(5 votes)
- any other videos explaining this type of math? I have no idea whats going on(4 votes)
- Hi all, wish you guys luck.(4 votes)
my teachers taught me a whole different way to do the problem dealing with isolating quantities harder example. can someone please confirm what the recommended way to do this is?(1 vote)
Well, what way did your teacher teach you? Just use the one you're comfortable with.(4 votes)
Isn't one raised to any power 1? So why couldn't the answer be c?(2 votes)- From the author:Interesting question, Devonique! You are correct that 1^(1/t) would be 1, but remember that (x-y)^2 does not equal x^2 - y^2. So, if you were write out choice C and multiply it out using the FOIL technique, you would have a messy middle term – the equivalent of the -2xy term in my quadratic example. So, choices C and D are not equivalent. To prove this further, you could plug in some values for A, P, and t and see if r comes out differently for each choice.(2 votes)
Has Sal ever talked to anyone in the questions or comments?(2 votes)
At1:39i didn't really get what tutor did....can someone please explain?(2 votes)
What is the difference in solving for just the t power vs the 1/t power? Like, what would happen if t was subbed for 2?(2 votes)
1:21Video transcript
- [Instructor] If an
initial investment, P, bears interest at a rate r, so this initial investment P, bears interest at a rate R,
and is compounded annually, its future value A, after t years, can be determined with the equation above. Which of the following equations
shows the interest rate in terms of the future
value, initial investment, and number of years invested? So they really just
want us to solve for r. So let's see if we can do that. So we have the future value, gonna give myself some space. Future value is equal,
I'm just rewriting it, is equal to the initial investment times one plus our interest rate, and then that quantity to the t power. So let's see what we can do. So the first thing I could do is I can get the P onto the left-hand side by dividing both sides of this equation by our initial investment. So if I do that, I get, and actually, let me, let
me swap the sides, too. Then I get one plus r to the t power is equal to our future value divided by our initial investment. Now, how do I get rid of
this to the t power here? Well, I can raise both sides
to the one over t power. So I could raise that
to the one over t power. One over t. By doing the left side, I have to do it to the
right side, as well. So on the left-hand side, if I raise something to the t and then I raise it to the one over t, remember, if you raise
something to an exponent and then raise it to another exponent, you're raising it to the
product of these two exponents. So this is equivalent to raising one, this is equivalent to
just raising one plus r to the first power, or this is just going to
simplify to one plus r on the left-hand side. And on the right-hand side, we're gonna have our future value divided by our initial investment to the one over t power. And now, pretty straightforward. You wanna solve for r, subtract one from both sides. We get r is equal to our future value divided by our initial investment to the one over t power minus one. And that is this choice right over there.