Is f(x) = 0.69(1.03)x a decreasing or increasing function?

Question

rea201 · Answer

All you need to do for this problem is graph the equation

anonymous · Answer

ohh thanks

rea201 · Answer

Desmos is a really good online grapher. If you graphed the equation you would see that the equation is increasing.

rea201 · Answer

Also can you give me a medal?

rea201 · Answer

all you have to do is click the best response button

anonymous · Answer

there you go :)

rea201 · Answer

Thanks!!

solomonzelman · Answer

no need for graphing

anonymous · Answer

oh wait by what percent?

solomonzelman · Answer

$\large\color{black}{  f(x) = 0.69(1.03)^x}$

when $\large\color{black}{x=1}$, then you have: $\large\color{black}{   0.69 \times1.03}$ 
when $\large\color{black}{x=2}$, then you have: $\large\color{black}{   0.69 \times 1.03 \times 1.03}$ 
when $\large\color{black}{x=3}$, then you have: $\large\color{black}{   0.69 \times 1.03 \times 1.03 \times 1.03}$ 
when $\large\color{black}{x=4}$, then you have: $\large\color{black}{   0.69 \times 1.03 \times 1.03 \times 1.03\times 1.03}$ 

and on

solomonzelman · Answer

right?

anonymous · Answer

yeah

solomonzelman · Answer

so each time (as $\large\color{black}{  x}$  increases by $\large\color{black}{   1}$ ) you multiply times $\large\color{black}{   1.03}$

solomonzelman · Answer

that means that the function is increasing.

solomonzelman · Answer

because anytime, when you multiply a(ny) number $\large\color{black}{  C}$ by a number greater than 1, then the result will be greater than this number $\large\color{black}{  C}$ .

solomonzelman · Answer

So for any exponential function $\large\color{black}{ y=a(b)^x}$         (when $\large\color{black}{ a}$ is positive)

~ when $\large\color{black}{b>0}$ , the $\large\color{black}{ f(x)}$ is increasing.
~ when $\large\color{black}{b<0}$ , the $\large\color{black}{ f(x)}$ is decreasing.

anonymous · Answer

okay and by what percent is it increasing?

solomonzelman · Answer

okay, you are multiplying times $\large\color{black}{ 1.03}$ , which is same as taking $\large\color{black}{ 103 \text{%}}$ (of the previous input) each time.

solomonzelman · Answer

$\large\color{black}{ 100 \text{%}}$ is what you had, and $\large\color{black}{ +3 \text{%}}$ is the extra part.

anonymous · Answer

ohh ok ok I get that was helpful thank you!

solomonzelman · Answer

yw