Question

Write an exponential function that could model the information in this graph....

Answer 1

y=Ae^(bx)

is a general exponential function

Answer 2

now you have the point (0,1) what does it tell you ?

Answer 3

(what can you find using this point)

Answer 4

its e^x
cz e^x passes from 1

Answer 5

i am honestly not quite sure

Answer 6

miteshchvm is wrong by the way

Answer 7

ok lets use (0,1) we plug it into the general function y=Ae^(bx)

we get :
y(0) = Ae^0 = A
and we know that it should be 1
so A = 1

Answer 8

so our function become y=e^(bx)

agree so far ?

Answer 9

yeah i do

Answer 10

good so now we will use the other point
(1,2)

in the same manner what will we have ?

Answer 11

base is 2

Answer 12

not e

Answer 13

yes ofcurse .. but we will find it out using this way

Answer 14

and as i said the one who said that the answer is e^x is wrong ..

Answer 15

im confused

Answer 16

keep going ..

now we have y = e^(bx)

we will use the other point
(1,2)

in the same manner what will we have ?

Answer 17

moni ? are you trying to do it ?

Answer 18

yeah i am... I'm just confused

Answer 19

ok lets do it together ..
plugging the point (1,2) into the function we have y=e^(bx) we get :

2 = e^b

right ?

Answer 20

yes

Answer 21

can you tell what is b now ?

Answer 22

be would be 1 right?

Answer 23

no.. why would you say so ? e is not 2 !

Answer 24

e = 2.718...

Answer 25

in order to find b from :
2 = e^b
you have to take Ln of both sides
do you know how to do it ?

Answer 26

honestly no because my math book didn't cover this

Answer 27

i think it's better to know it before solving such questions
havent you seen this for example :
\[\ln (x^a) = a \ln (x) \]

Answer 28

i think I've seen it before

Answer 29

Logarithm laws*
so doing here we get

ln(2) = ln(e^b)
ln(2) = bln(e)

and since the base of ln is e we know that ln(e)

and we get ln(2) = b

Answer 30

ok i follow

Answer 31

now plugging it into our function we have

y = e^(xln(2))

using the above logarithm law we may say :

y= e^(ln(2^x))

right ?

Answer 32

right..

Answer 33

now there is another law we may use and it is :
\[e^{\ln(a)} = a\]

Answer 34

whenever you raise a number to a power which is a logarithm with the base of the same number the result is the argument inside the logarithm .. maybe you saw this law as well