Answer/Discussion on Exponential Functions

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College Algebra
Answer/Discussion to Practice Problems
on Exponential Functions

Answer/Discussion to 1a

Try this using your calculator and see if you get the answer that I got. If you didn't, refer back to e key on calculator that I have above.

(return to problem 1a)

Answer/Discussion to 1b

Try this using your calculator and see if you get the answer that I got. If you didn't, refer back to e key on calculator that I have above.

(return to problem 1b)

Answer/Discussion to 2a

Note that the base = 5 and the exponent is our variable x + 1. There is one outside factor, we are adding 1 to our variable x in the exponent

Step 1: Find ordered pairs.

I have found that the best way to do this is to do it the same each time. In other words, put in the same values for x each time and then find it's corresponding y value for the given function.

x		(x, y)
-2		(-2, .2)
-1		(-1, 1)
0		(0, 5)
1		(1, 25)
2		(2, 125)

Step 2: Plot points.
AND
Step 3: Draw curve.

(return to problem 2a)

Answer/Discussion to 2b

Note that the base = 1/5 and the exponent is our variable x. There are 2 outside factors, we are multiplying it by -5 AND we are adding 2 to our base after we raise it to the exponent x and multiply that by -5.

Step 1: Find ordered pairs.

I have found that the best way to do this is to do it the same each time. In other words, put in the same values for x each time and then find it's corresponding y value for the given function.

x		(x, y)
-2		(-2, -123)
-1		(-1, -23)
0		(0, -3)
1		(1, 1)
2		(2, 1.8)

Step 2: Plot points.
AND
Step 3: Draw curve.

(return to problem 2b)

Answer/Discussion to 3a

$7500 for 25 years at an annual rate of 4.25% compounded monthly.

P = 7500
r = 4.25% = .0425
t = 25
n = monthly = 12 times a year

*Plug in values shown above into compound form.

*Find number inside the ( ) first

*Raise the ( ) to the 300th power
*Multiply

So the compound AMOUNT would be $21661.27

The compound amount is the total amount that is in the account. How do you think we are going to get the interest?? Well we have the principle which is the beginning amount and we have the compound amount which is the end result. Looks like, if we take the difference of the two, that will give us how much interest was earned from beginning to end. What do you think?

Compound amount - principle: 21661.27 - 7500 = 14161.27

So our compound interest is $14161.27

(return to problem 3a)

Answer/Discussion to 3b

$3000 for 20 years at an annual rate of 6% compounded quarterly.

P = 3000
r = 6% = .06
t = 20
n = quarterly = 4 times a year