Question

math problem

Answer 1

@snowflake0531

Answer 2

@florisalreadytaken

Answer 3

exponential function form

\(f(x) = a^x\)

Answer 4

is it not \[ f(x) = a \times b^x\] ?

Answer 5

whos right

Answer 6

following the one Andreas suggested, it will be a very long and hard t understand explanation lol -- so lets go with mine -- lowe me a moment to write it down

Answer 7

alright

Answer 8

\[y=a(b)^x\]

Answer 9

so, an exponential function is in the form of: \( y = a \times b^x \)

we are given:
\[ x=2 \; ; \; y=-12 \]
and
\[ x=3 \; ; \; y=-24 \]

for the first one we have:
\[ -12= a \times b^2 \]
\[ a= \frac{-12}{b^2} \]
looking at the first equation, we plug ^ that in for \(a\):
\[ y=(\frac{-12}{b^2}) \times b^x \]

Answer 10

I simplify y=(-12/b^2)*b^x

Answer 11

1

Answer 12

nono.

substitue the coordinates of the 2nd point, and then solve for b:
\[ -24=(\frac{-12}{b^2}) \times b^3 \]
do the math

Answer 13

im not sure

Answer 14

b = 2

Answer 15

ahh my whole latex went in the bin😭😂 -- but yes, \( b=2 \)

Answer 16

do you remember \( a= \frac{-12}{b^2} \)?

now we can fully solve for a.
\[ a= \frac{-12}{2^2} \]
\[ \underline{a=-3} \]

Answer 17

so we have
\[ a=\color{lightskyblue}{-3} \]
and
\[ b=\color{tomato}{2} \]

Answer 18

what? noooo

Answer 19

plugging that info in the formula, we get

\[ \Large f(x) = \color{tomato}{2} \times \color{lightskyblue}{ -3}^x


\]
\[ \updownarrow \]

\[ \Large f(x) = \color{tomato}{2} \times \color{lightskyblue}{( -3)}^x \]

Answer 20

thanks

Answer 21

you got it!

Answer 22

oh, maybe the \( \times \) sign is not necessary

Answer 23

that doesnt make sense :\ -- and you missed the exponential \(x\) in your answer

Answer 24

lol