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# is it f(x)=3(5/3)^-x ​ a exponential growth function?

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is it f(x)=3(5/3) a exponential growth function?

Dec 11, 2015

#1
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is it f(x)=3(5/3)^-x a exponential growth function?

$$\begin{array}{rcll} f(x) &=& 3 \cdot \left( \frac53 \right)^{-x} \\ f(x) &=& 3 \cdot \frac{1} { \left( \frac53 \right)^x } \\ f(x) &=& 3 \cdot \frac{1} { \frac{5^x}{3^x} } \\ f(x) &=& 3 \cdot \frac{3^x} { 5^x } \\ f(x) &=& 3 \cdot \left( \frac35 \right)^x \\ \end{array}$$

No it is a decaying function, because: $$\frac35 < 1$$

$$y=a\cdot b^x\\ \text{Example: } y = 3 \cdot \left( \frac35 \right)^x$$

when a > 0 and the b is between 0 and 1, the graph will be decreasing (decaying).

Dec 11, 2015

#1
+24947
+10

is it f(x)=3(5/3)^-x a exponential growth function?

$$\begin{array}{rcll} f(x) &=& 3 \cdot \left( \frac53 \right)^{-x} \\ f(x) &=& 3 \cdot \frac{1} { \left( \frac53 \right)^x } \\ f(x) &=& 3 \cdot \frac{1} { \frac{5^x}{3^x} } \\ f(x) &=& 3 \cdot \frac{3^x} { 5^x } \\ f(x) &=& 3 \cdot \left( \frac35 \right)^x \\ \end{array}$$

No it is a decaying function, because: $$\frac35 < 1$$

$$y=a\cdot b^x\\ \text{Example: } y = 3 \cdot \left( \frac35 \right)^x$$

when a > 0 and the b is between 0 and 1, the graph will be decreasing (decaying).

heureka Dec 11, 2015