Notes
Problems & Videos
Find the exponential function through the following points.
\(\textbf{1)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0, 5)\) and \((2, 20) \)
The answer is \( f(x)=5(2)^{x}\)
\(\text{Parent Function}\)
\(\,\,\,\,\,\,f(x)=a\cdot(b)^x\)
\(\text{Plug in the point} (0,5)\)
\(\,\,\,\,\,\,5=a\cdot(b)^0\)
\(\,\,\,\,\,\,5=a\cdot1\)
\(\,\,\,\,\,\,a=5\)
\(\text{Plug in for }a\)
\(\,\,\,\,\,\,f(x)=5\cdot(b)^x\)
\(\text{Plug in the point} (2,20)\)
\(\,\,\,\,\,\,20=5\cdot(b)^2\)
\(\,\,\,\,\,\,4=(b)^2\)
\(\,\,\,\,\,\,\pm2=b\)
\(\,\,\,\,\,\,b=2 \left(\text{note: }b\gt0 \right)\)
The answer is \( f(x)=5(2)^{x}\)
\(\text{Parent Function}\)
\(\,\,\,\,\,\,f(x)=a\cdot(b)^x\)
\(\text{Plug in the point} (0,5)\)
\(\,\,\,\,\,\,5=a\cdot(b)^0\)
\(\,\,\,\,\,\,5=a\cdot1\)
\(\,\,\,\,\,\,a=5\)
\(\text{Plug in for }a\)
\(\,\,\,\,\,\,f(x)=5\cdot(b)^x\)
\(\text{Plug in the point} (2,20)\)
\(\,\,\,\,\,\,20=5\cdot(b)^2\)
\(\,\,\,\,\,\,4=(b)^2\)
\(\,\,\,\,\,\,\pm2=b\)
\(\,\,\,\,\,\,b=2 \left(\text{note: }b\gt0 \right)\)
The answer is \( f(x)=5(2)^{x}\)
\(\textbf{2)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,-60)\) and \((2,-15) \)
The answer is \( f(x)=-60(.5)^{x}\)
\(\textbf{3)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,2)\) and \((3,54) \)
The answer is \( f(x)=2(3)^{x}\)
\(\textbf{4)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,9)\) and \((2,81) \)
The answer is \( f(x)=9(3)^{x}\)
\(\textbf{5)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,16)\) and \((4,1) \)
The answer is \( f(x)=16(0.5)^{x}\)
\(\textbf{6)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,-8)\) and \((3,-1) \)
The answer is \( f(x)=-8(0.5)^{x}\)
\(\textbf{7)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,81)\) and \((4,16) \)
The answer is \( f(x)=81(2/3)^{x}\)
\(\textbf{8)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,8)\) and \((3,27) \)
The answer is \( f(x)=8(3/2)^{x}\)
\(\textbf{9)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,24)\) and \((3,81) \)
The answer is \( f(x)=24(3/2)^{x}\)
\(\textbf{10)}\) Find the exponential function \(f(x)=a(b)^x\) through \( (0,18)\) and \((2,8) \)
The answer is \( f(x)=18(2/3)^{x}\)
