Question

Which exponential function has a growth factor of ?

Answer 1

Letter B would be the correct answer

Answer 2

Answer:

So, only option-c and option-d are same

Step-by-step explanation:

(a) From Graph:

Firstly, we will find function of the graph

Let's assume exponential function as

$f(x)=a(b)^x$

we can select any two points and find 'a' and 'b'

$f(0)=\frac{1}{2}$

At x=0 , y=1/2:

we can plug values

$f(0)=a(b)^0$

$\frac{1}{2}=a(b)^0$

$a=\frac{1}{2}$

now, we can plug it back

and we get

$f(x)=\frac{1}{2}(b)^x$

At x=-1 , y=2:

we can plug values

$f(-1)=\frac{1}{2}(b)^{-1}$

$2=\frac{1}{2}(b)^{-1}$

$b=\frac{1}{4}$

now, we can plug it back

and we get

$f(x)=\frac{1}{2}(\frac{1}{4})^x$

(b) From chart:

Firstly, we will find function of the graph

Let's assume exponential function as

$f(x)=a(b)^x$

we can select any two points and find 'a' and 'b'

$f(0)=\frac{1}{2}$

At x=0 , y=1/2:

we can plug values

$f(0)=a(b)^0$

$\frac{1}{2}=a(b)^0$

$a=\frac{1}{2}$

now, we can plug it back

and we get

$f(x)=\frac{1}{2}(b)^x$

At x=1 , y=1:

we can plug values

$f(1)=\frac{1}{2}(b)^{1}$

$1=\frac{1}{2}(b)^{1}$

$b=2$

now, we can plug it back

and we get

$f(x)=\frac{1}{2}(2)^x$