1. Consider the functions shown below. A. f(x) =...

1. Consider the functions shown below. A. $f(x) = (1.023)^x$ B. $f(x) = 320(0.95)^x$ C. $f(x) = 400(1.12)^x$ F. $f(x) = 8452(0.67)^x$ D. $f(x) = 34.9(1.11)^x$ E. $f(x) = 172(0.99)^x$ a) Which functions are increasing? b) Which function is increasing at the fastest rate? What is the growth rate for this function? c) Which function is decreasing at the fastest rate? What is the decay rate for this function? 2. Fred and Wilma purchase a home for $180,000. Using function notation, write a linear or exponential equation for the value, $V$, of the house $r$ years after its purchase, assuming that the value: a) Decreases by $1,500 per year. b) Decreases by 2% per year. c) Increases by $3,100 per year. d) Increases by 6% per year

Transcript

00:01 So in this table, we want to fill in the following functions, given the initial value, the growth or decay rate.

00:07 So remember, for your exponential function, divinely with your growth and decay rate, f of x, will equal to your initial value, i'll call i.

00:15 And it's multiplied by one plus or minus.

00:20 Your growth rate all raised to the x power.

00:24 So, and for the first one, when our initial value is 90, that means we're going to have 90.

00:29 And in parentheses, we'll have one.

00:31 Well, because it's growth rate, we're going to add.

00:33 And remember, we have to current 29 % to a decimal.

00:36 So we move it two places to the left, so we have 0 .29, all raised to the x power.

00:41 So that would be your first function.

00:43 All right, let's look at the second one.

00:45 Our initial value is 117.

00:47 Again, it's going to be a growth rate, and it's equal to 5%.

00:53 So again, we're going to have f of x equal.

00:55 Our initial value would be 117.

00:58 It's a growth rate, so we're going to have 1 plus, and 5 % is a decimal, we move the decimal .2 places to the left, so we have 0 .05.

01:06 And again, it's all raised to the x value.

01:08 So that would be the second one.

01:11 Okay, now for the third one, we're going to have 137 is the initial value.

01:15 We're going to have a growth rate again, and this time our growth rate is equal to 4 .5%.

01:21 So now let's write our function.

01:23 So again, it's the initial value, 137.

01:26 It's a growth rate, so we'll have 1 plus, and now we turn 4 .5 to a decimal.

01:32 Move with the decimal point two places to the left.

01:34 So it would be 0 .045.

01:36 I'll raise to the x power.

01:39 So that would be the third.

01:41 All right.

01:41 So now let's go to the fourth example.

01:44 So for the fourth example, our initial value is 55.

01:47 In this case, again, it's going to be a growth rate...

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