# How do you find formula for the exponential function in the form of f(x)= Ca^x given f(0)=3 and f(1)=15?

##### 3 Answers
Jul 22, 2018

$\textcolor{b l u e}{f \left(x\right) = 3 \cdot {5}^{x}}$

#### Explanation:

We have:

$C {a}^{0} = 3$

$C {a}^{1} = 15$

$C {a}^{0} = 3 \implies C = 3$

So:

$3 a = 15 \implies a = 5$

This gives:

$f \left(x\right) = 3 \cdot {5}^{x}$

Jul 22, 2018

$f \left(x\right) = 3 {\left(5\right)}^{x}$

#### Explanation:

$\text{substitute "(0,3)" into the equation}$

$C {a}^{0} = 3 \Rightarrow C = 3$

$\text{substitute "(1,15)" into the equation}$

$3 {a}^{1} = 15 \Rightarrow a = \frac{15}{3} = 5$

$f \left(x\right) = 3 {\left(5\right)}^{x}$

Jul 22, 2018

$f \left(x\right) = 3 \cdot {5}^{x}$.

#### Explanation:

Let, $f \left(x\right) = c {a}^{x}$.

$\text{Given that } f \left(0\right) = 3 \Rightarrow c {a}^{0} = 3 \Rightarrow c = 3$.

$\therefore f \left(x\right) = c {a}^{x} = 3 {a}^{x}$.

$\text{Also } f \left(1\right) = 15 \Rightarrow 3 {a}^{1} = 15 \Rightarrow a = 5$.

$\text{Thus, } f \left(x\right) = c {a}^{x} , c = 3 , a = 5$.

$\Rightarrow f \left(x\right) = 3 \cdot {5}^{x}$.