1. Home
  2. Algebra and trigonometry
  3. Exponential and logarithmic
  4. Exponential functions

6.1 Exponential functions  (Page 6/16)

<< Chapter < Page
  Algebra and trigonometry     Page 6 / 16
Chapter >> Page >

Find an equation for the exponential function graphed in [link] .

Graph of an increasing function with a labeled point at (0, sqrt(2)).

f ( x ) = 2 ( 2 ) x .   Answers may vary due to round-off error. The answer should be very close to   1.4142 ( 1.4142 ) x .

Got questions? Get instant answers now!

Given two points on the curve of an exponential function, use a graphing calculator to find the equation.

  1. Press [STAT].
  2. Clear any existing entries in columns L1 or L2.
  3. In L1 , enter the x -coordinates given.
  4. In L2 , enter the corresponding y -coordinates.
  5. Press [STAT] again. Cursor right to CALC , scroll down to ExpReg (Exponential Regression) , and press [ENTER].
  6. The screen displays the values of a and b in the exponential equation   y = a ⋅ b x .

Using a graphing calculator to find an exponential function

Use a graphing calculator to find the exponential equation that includes the points   ( 2 , 24.8 )   and   ( 5 , 198.4 ) .

Follow the guidelines above. First press [STAT] , [EDIT] , [1: Edit…], and clear the lists L1 and L2 . Next, in the L1 column, enter the x -coordinates, 2 and 5. Do the same in the L2 column for the y -coordinates, 24.8 and 198.4.

Now press [STAT] , [CALC] , [0: ExpReg] and press [ENTER] . The values   a = 6.2   and   b = 2   will be displayed. The exponential equation is   y = 6.2 ⋅ 2 x .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Use a graphing calculator to find the exponential equation that includes the points (3, 75.98) and (6, 481.07).

y ≈ 12 ⋅ 1.85 x

Got questions? Get instant answers now!

Applying the compound-interest formula

Savings instruments in which earnings are continually reinvested, such as mutual funds and retirement accounts, use compound interest    . The term compounding refers to interest earned not only on the original value, but on the accumulated value of the account.

The annual percentage rate (APR)    of an account, also called the nominal rate    , is the yearly interest rate earned by an investment account. The term  nominal  is used when the compounding occurs a number of times other than once per year. In fact, when interest is compounded more than once a year, the effective interest rate ends up being greater than the nominal rate! This is a powerful tool for investing.

We can calculate the compound interest using the compound interest formula, which is an exponential function of the variables time   t , principal   P , APR   r , and number of compounding periods in a year   n :

A ( t ) = P ( 1 + r n ) n t

For example, observe [link] , which shows the result of investing $1,000 at 10% for one year. Notice how the value of the account increases as the compounding frequency increases.

Frequency Value after 1 year
Annually $1100
Semiannually $1102.50
Quarterly $1103.81
Monthly $1104.71
Daily $1105.16

The compound interest formula

Compound interest can be calculated using the formula

A ( t ) = P ( 1 + r n ) n t

where

  • A ( t )   is the account value,
  • t   is measured in years,
  • P   is the starting amount of the account, often called the principal, or more generally present value,
  • r   is the annual percentage rate (APR) expressed as a decimal, and
  • n   is the number of compounding periods in one year.

Calculating compound interest

If we invest $3,000 in an investment account paying 3% interest compounded quarterly, how much will the account be worth in 10 years?

Because we are starting with $3,000,   P = 3000.   Our interest rate is 3%, so   r   =   0.03.   Because we are compounding quarterly, we are compounding 4 times per year, so   n = 4.   We want to know the value of the account in 10 years, so we are looking for   A ( 10 ) , the value when   t   =   10.

A ( t ) = P ( 1 + r n ) n t Use the compound interest formula . A ( 10 ) = 3000 ( 1 + 0.03 4 ) 4⋅10 Substitute using given values . ≈ $ 4045.05 Round to two decimal places .

The account will be worth about $4,045.05 in 10 years.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 4

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask