Seamus bought a car that originally sold for 40,000 . It exponentially depreciates at a rate of

step 1 All right, everyone. Welcome. Today we're looking at a question about a car that was purchased f

Seamus bought a car that originally sold for 40,000 . It...

Key Concepts

Exponential Decay Equation

This concept refers to a mathematical formula that models processes where the quantity decreases by a constant percentage over equal time intervals. It is typically expressed as A(t) = A? * (1 - r)?, where A? represents the initial amount, r is the rate of decay per time interval, and t is the number of time intervals.

Depreciation

Depreciation is the reduction in the value of an asset over time. When modeled exponentially, it implies that the value decreases by a fixed percentage each period, reflecting the gradual loss in market value or utility of the asset over time.

Decay Rate

The decay rate is the fixed proportion by which a quantity diminishes over each time period in an exponential decay model. It is essential for determining the decay factor, which is calculated as (1 - r), used within the exponential decay equation to compute the remaining value after a given time.

Transcript

00:01 All right, everyone.

00:02 Welcome.

00:03 Today we're looking at a question about a car that was purchased for $40 ,000 and has a depreciation rate of 7 .75 % annually.

00:17 All right.

00:18 And so a couple of things that we want to identify here in this question.

00:21 First of all, this $40 ,000 here.

00:24 This represents the present value of the car.

00:29 Okay.

00:30 So the present value of the car.

00:31 Meaning that this is, you know, the value of the car when the person buys it before any time has gone on.

00:38 Okay, so that's what the car is worth when the person gets it.

00:42 But in the future, that value is going to change.

00:45 When values have an appreciation rate, then you can expect them to increase in value.

00:51 But in this case, because it's a car and cars are not typically good investments, they don't gain interest, they lose value.

01:00 And so in this situation it's going to be decreasing by a rate of 7 .75 percent.

01:08 Okay, another thing that we want to do here is convert our percentage into decimal form, just so that it works into our equation.

01:17 And so, of course, 7 .75 % divided by 100 is going to give me my answer in decimal form, which is 0 .0775.

01:30 So that's my rate of change that's going to be taken place.

01:35 And because it's depreciation, this will actually be a negative rate here, at least in the equation that we're going to use, which is the equation below here...

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