Question 468317
Given the exponential function:
{{{y = a*b^x}}}
where a is a constant scale factor and b is the base raised to power of x.
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If b > 1, then as x increases so does y, thus its a growth function.
Ex:
a=1, b=2
{{{y = 2^x}}}
If x = 1, y = 2^1 = 2
If x = 3, y = 2^3 = 8
...
{{{graph(200,200,-1,5,-1,20,2^x)}}}
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If b < 1, then as x increases y decreases, thus its a decay function.
Ex:
a=1, b=1/2
{{{y = (1/2)^x}}}
If x = 1, y = (1/2)^1 = 1/2
If x = 3, y = (1/2)^3 = 1/8
...
{{{graph(200,200,-1,5,-1,2,0.5^x)}}}
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Remember:
b > 1 ---> Growth
b < 1 ---> Decay
You can always check by plugging in x_values as well, I suggest 0 and 1.
If the y_value went up then its growth, if not its decay.
Lets look at your problem {{{y = 11(8/13)^x}}}
a= 11, b = 8/13
8/13 < 1 --> Decay
{{{y = 11(8/13)^0 = 11}}}
{{{y = 11(8/13)^1 = 88/13 = 6.77}}}
y decreased therefore we confirm the function is a decay function.