Question

Please help, im going to cry. Find a formula for the exponential function which satisfies the given conditions:
g(10)=70 and g(30)=10

Answer 1

I have no clue what im doing

Answer 2

do you know what the general form of an exponential function looks like.

Answer 3

yes f(x) = a(b)^x

Answer 4

So f(x) is 70 and 10, the x is the 10 and 30

Answer 5

\[70 = ab^{10}\]\[10 = ab^{30}\]

Answer 6

a b^(x-h) + k is what i was thinking

Answer 7

thats vertex form?

Answer 8

nvm lol

Answer 9

dunno the name of it, it just covers all the possible shifts and scalars

Answer 10

we don't have enuf info to use your formula @amistre64

Answer 11

bummer .... im not opposed to h,k = 0,0

Answer 12

@TheRealBMH .. so take the log of both side of both equation and solve.

Answer 13

what does the log of ab^2 look like?

Answer 14

loga +2 logb

Answer 15

1.85 = loga + 2 logb?

Answer 16

where you get 2 from though????

Answer 17

we could sub it as well, then log out of it maybe

70/b^10 = a

10 = 70b^(20)

Answer 18

from you lol

Answer 19

ohhh xD

Answer 20

x*

Answer 21

substituting first seems better :)

Answer 22

where di the 20 come from?

Answer 23

b^(30)
------
b^(10)

Answer 24

solving for a, then subing it in

Answer 25

30 bs, canceled by 10 bs leaves 20 bs

Answer 26

ok so a is 20 now we just solve for b?

Answer 27

70 = a b^10 , solve for a by dividing off b^10

a = 70/b^10

sub this into the other setup

10 = a b^30

10 = 70 b^20

1/7 = b^20, not take the 20th rt

b = (1/7)^(1/20)

Answer 28

*now take ....

Answer 29

is spose since 20 is even, it should be +- 1/7 but i never worryabout stuff like that

Answer 30

so 20(1/7)^(1/20) ?

Answer 31

i feel so dumb

Answer 32

1/7 = b^20, not take the 20th rt
you have to be careful here?

Answer 33

the sign of b

Answer 34

so i just leave b how it is??

Answer 35

well, we know a value for b, and since b gets smaller as x gets bigger, lets go negative

and a = 70/b^10

a = -70/(1/7)^(1/20)

Answer 36

=-63.5

Answer 37

forgot the ^10

a = -70/(1/7)^(1/2)

Answer 38

-185.2

Answer 39

and b was 20?

Answer 40

1/7 = b^(20)

Answer 41

but how do i get it to f(x) = ab^2

Answer 42

why do you need it as ^2 ?

Answer 43

ab^2 is not an exponential function of x

Answer 44

a b^x is

Answer 45

ab^x

Answer 46

sorry idk why i keep saying that

Answer 47

we are solving for a and b

Answer 48

right

Answer 49

a = 70sqrt(7)
b = +- (1/7)^(1/20)

b^x = +- [(1/7)^(/20)]^x

Answer 50

is that meant to be 20 or .20 on the last part

Answer 51

(/20)

Answer 52

(1/20) i was wanting to do multiply by x and make it x/20 but my fingers protested

Answer 53

http://www.wolframalpha.com/input/?i=70%3Dab%5E%2810%29%2C+10%3Dab%5E%2830%29

Answer 54

b has to be positive in an exponential function... no +/-

Answer 55

exactly, thank you for pointing that out, i appreciate your help dude

Answer 56

thanks for being patient and really helping and explaining @amistre64 i really appreciate it!

Answer 57

youre welcome, im glad the site didnt mess up to bad along the way