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### Course: Digital SAT Math > Unit 8

Lesson 10: Quadratic and exponential word problems: medium- Quadratic and exponential word problems | Lesson
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems: medium

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# Interpreting nonlinear expressions — Basic example

Watch Sal work through a basic Interpreting nonlinear expressions problem.

## Want to join the conversation?

- Since the SAT is timed, would it be wiser to use his second method rather than first because it saves time?(60 votes)
- Yes, Sal explains multiple methods to solve the problems and you would pick the one you prefer the most.(49 votes)

- Ain't there shortcut methods. Khan academy solves questions in a way that it consumes lots of time.(38 votes)
- Yes, Sal tries to solve selected random problems on the SAT in a more detailed manner.(8 votes)

- These kinds of problems always sound confusing to me. Guess I just have to slow down and read clearly.(13 votes)
- this is in no way a basic example.the video is suppose to help you but this is something else(13 votes)
- I still don't get why he multiplied it by the 10^6 to the 0.75. Please explain.(4 votes)
- He used the law of exponents-(a^m)^n=a^mn(7 votes)

- One question. All these topics could be either in the section with calculator or that without? So you have to know how to do them without calc? Are there exceptions?(8 votes)
- you can use a calculator on both sections of the digital SAT.(1 vote)

- what do -4.9t^2 and 8t represent?(3 votes)
- If you've taken a physics class before, one of the kinematic equations is Δx = V_0*t + 1/2 at^2. This relates the change in position to an initial velocity and an acceleration. For a projectile (like the basketball thrown up into the air), the acceleration would be the force of gravity, or 9.8 m/s^2. The initial velocity is what the ball has because of being thrown upwards. The displacement can be broken down to the difference between the projectile's height (h(t)), and an initial height (1.2). We can then modify the equation to look like what you have in the question:

Δx = V_0*t + 1/2at^2

h(t) - h_0 = 8t + 1/2 (-9.8)t^2

h(t) = -4.9t^2 + 8t + 1.2

Of course, you don't need to know where any equation that you see on the SAT comes from in order to answer the question correctly.(6 votes)

- Simple elimination would solve this question in about 15 seconds.

A wouldn't work because the metabolic rate of the elephant is greater than that of the mouse.

B wouldn't work for the same reason, as it is stating the mouse's metabolic rate is faster.

C is possible, as the elephant's metabolism is stated to be faster.

D wouldn't work, as the base body mass is multiplied by an exponent and the final value will not be in the same proportions.(2 votes)- Nice logic! Unfortunately, not everybody will be able to narrow down a question to one answer just like that, and almost no one would be able to do so for every question, which is why the video exists. But doing great on the SAT is really all about finding these shortcuts that allow you to choose answers quickly and with certainty.(6 votes)

- Before I ask my question I just want to mention that I'm writing this on a phone. If there are any grammer mistakes, I apologize.

My question regards the answer explanations of the level 4 questions for the "interpreting nonlinear functions" category.

For one of the problems, I wrote the following on my whiteboard: 🔺️m = k(1/4*T)^2 / 2*pi ; 🔺️m = k*(1/4)^2 *T^2 / 2*pi ; 🔺️m = k(1/16)*T^2 / 2*pi .

I can't remember if I choose the correct answer, but the answer explanation had the equation written as follows: m(new) = k(1/4*T)^2 / 2*pi ; m(new) = (1/16) * ((k*T^2) / 2*pi).

My question is how did the 1/16 change places in the equations in the answer explanation. The step is missing from the explanation and I'm confused as a result.(3 votes)- I thought I would add something that might help anyone who's still confused. I emailed one of my former math teachers about this and she said it seemed correct, so I thought I'd share. Please feel free to comment any corrections if I made a mistake.

m = kT^2 / 2*pi

The mass changes and the period of oscillation, T, is reduced by 1/4. Find the accurate description for the change in mass. (There is more context to this problem that I didn't write down on my whiteboard. Also, this was a multiple choice question. Basically, choose the correct answer that accurately describes the change in mass given the above info.).

So,

m(new) = k(1/4T)^2 / 2*pi

We square both T and 1/4:

m(new) = k *(1/4)^2 *T^2 / 2*pi

m(new) = k(1/16)*T^2 / 2*pi

For the sake of organization and because the commutative property of multiplication allows it, we can take 1/16 out to get:

m(new) = (1/16)/1 * kT^2/2*pi

(1/16)/1 --> (1/16)/(1/1) --> (1/16)*(1/1) --> 1/16

so,

m(new) = (1/16) * kT^2/2*pi

since m = kT^2/2*pi, we can replace kT^2/2*pi with m to get:

m(new) = (1/16)*m

The new mass is 1/16 of the original mass.

Hope this helps! If anyone notices any mistakes, please correct them! :)(3 votes)

- What is the definition of basal metabolic(4 votes)

## Video transcript

- [Instructor] We're
told the function above models the height h, in meters, of a basketball above ground t seconds after being thrown straight up in the air. What does the number 1.2
represent in the function? So pause this video and
think about it on your own before we work through it together. All right, so we could just
visualize what's happening when you throw a basketball
straight up in the air. This is the ground. Let's say this is the person
throwing the basketball. This is the basketball. It starts at some height. So whatever height this is, that's its initial
height at t equals zero. And then, it's gonna be thrown
with some upward velocity. And it's initially going
to be a high velocity, but then it's gonna slow down. And then, at some point,
it's gonna be stationary, and then it's gonna start
accelerating back downwards. Now, as I mentioned, at t equals zero, what do we see over here? Well, let's see, h of zero is going to be equal
to, this term goes away, 'cause anything times zero is zero. That term goes away. And we're just left with 1.2, the exact number that
they're thinking about. So if you think about it, h of zero, this tells you the position of the ball, in terms of meters above the ground, right when we are starting. So it's telling us the
initial height of the ball. So let's see, it looks like that's exactly what they're saying for choice A, the initial height, in
meters, of the basketball. The maximum height in
meters of the basketball? No, that's definitely not saying that. The maximum height is not going to occur at t equals zero. It's going to occur sometime after that. Rule that one out. The amount of time in seconds the basketball remains airborne. No, that's not the case. Any value that h takes on, remember, h is in meters. T, which is an input into
the function, is time. So if you're talking about
something that h is equal to, which, in this case, h is equal to 1.2 and t is equal to zero, you're talking about a
height above the ground. And then the initial speed. Well, once again, no, this is h of zero, which is the height above the ground. So we like choice A.