Question

An exponential function in the form y=500(b)x contains the points (0,500) and (3,4). What is the value of b?

Answer 1

An exponential function in the form y=500(b)^x contains the points (0,500) and (3,4). What is the value of b?

Answer:

An exponential function in the form y=500(b)^x contains the points (0,500) and (3,4). Then the value of b is $\frac{1}{5}$

Solution:

Given that, An exponential function in the form $y=500(b)^{x}$ contains the points (0,500) and (3,4).  

We have to find what is the value of b

Now, as the function contains (0, 500), let us substitute it in given function.

$\begin{array}{l}{\rightarrow \quad 500=500 \times \mathrm{b}^{0}} \\\\ {\rightarrow \quad 1=\mathrm{b}^{0}}\end{array}$

Here, it is not possible to find b exact value, as anything power 0 is 1.

So, now let us go for the next point. i.e. (x, y) = (3, 4)

Substitute x = 3 in given function

$\begin{array}{l}{4=500 \times b^{3}} \\\\ {1=125 \times b^{3}} \\\\ {1=5^{3} \times b^{3}}\end{array}$

$\begin{array}{l}{1=(5 b)^{3}} \\\\ {(5 b)^{3}=1^{3}} \\\\ {5 b=1} \\\\ {b=\frac{1}{5}}\end{array}$

Hence, the value of b is $\frac{1}{5}$

Answer 2

Answer:

1/5

Step-by-step explanation:

Substitute the point (3,4) into the equation y=500(b)x to find the value of b.

41125=b3(15)3=500(b)3=b3

The value of b is 15.