Math Question

Carmelita’s grandmother offered to sponsor her money when she competed in her swim meeting. Her grandmother said that she will give her $1 if she swims 1 lap, $3 if she swims 2 laps, $5 if she swims 3 laps, $7 if she swims 4 laps, and so on. How much money will she have if her grandmother pays her for 20 laps?

Is this donation pattern an exponential function, linear function, or neither? Why?

Solution

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HOW MUCH MONEY WILL SHE HAVE WHEN HER GRANDMOTHER PAYS HER

FOR 20 LAPS?

Let the number of LAPS be the X value of ordered pairs.

Let the DOLLAR AMOUNT be the Y value of the ordered pairs.

LAPS MONEY

(1, 1)

(2, 3)

(3, 5)

(4, 7)

Notice that the Y value above is always an ODD number.

The FUNCTION RULE applied to the X value, resulting in the ODD NUMBER Y value is:

f(X) = 2X – 1.

So, f(1) = (2 * 1) – 1 = 2 – 1 = 1

f(2) = (2 * 2) – 1 = 4 – 1 = 3

f(3) = (2 * 3) – 1 = 6 – 1 = 5

f(4) = (2 * 4) – 1 = 8 – 1 = 7

For 20 LAPS, X = 20, we use the above function.

f(20) = (2 * 20) – 1 = 39

ANSWER: HER GRANDMOTHER GIVES HER $39

Is this donation pattern an exponential function, linear function, or neither?

f(X) is the same thing as the value of Y.

So, f(X) = 2X – 1 is the same as Y = 2X – 1.

Y = 2X – 1 IS A LINEar EQUATION. (Lowercase “ar” for emphasis.)

Why?

Not exponential because of the FUNCTION RULE 2X-1.

An example of an EXPONENTIAL FUNCTION would be f(X) = X^2 + 5.

Hope this helps Jason.