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

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 [tex]\frac{1}{5}[/tex]Solution:Given that, An exponential function in the form [tex]y=500(b)^{x}[/tex] contains the points (0,500) and (3,4).  We have to find what is the value of bNow, as the function contains (0, 500), let us substitute it in given function.[tex]\begin{array}{l}{\rightarrow \quad 500=500 \times \mathrm{b}^{0}} \\\\ {\rightarrow \quad 1=\mathrm{b}^{0}}\end{array}[/tex]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[tex]\begin{array}{l}{4=500 \times b^{3}} \\\\ {1=125 \times b^{3}} \\\\ {1=5^{3} \times b^{3}}\end{array}[/tex][tex]\begin{array}{l}{1=(5 b)^{3}} \\\\ {(5 b)^{3}=1^{3}} \\\\ {5 b=1} \\\\ {b=\frac{1}{5}}\end{array}[/tex]Hence, the value of b is [tex]\frac{1}{5}[/tex]