The form of the exponential function is
[tex]y=a(1\pm r)^x[/tex]a is the initial value
r is the rate in decimal
(+) for growth
(-) for decay
1.
The initial value is 153, then
[tex]a=153[/tex]The growth rate is 20%, then change it to decimal by dividing it by 100
[tex]r=\frac{20}{100}=0.2[/tex]Substitute them in the form above
[tex]\begin{gathered} y=153(1+0.2)^x \\ y=153(1.2)^x \end{gathered}[/tex]2.
The initial amount is 127
[tex]a=127[/tex]The rate of growth is 7%
[tex]r=\frac{7}{100}=0.07[/tex]The equation is
[tex]\begin{gathered} y=127(1+0.07)^x \\ y=127(1.07)^x \end{gathered}[/tex]3.
The initial value is 146
[tex]a=146[/tex]The growth rate is 5.5%
[tex]r=\frac{5.5}{100}=\frac{55}{1000}=0.055[/tex]The equation is
[tex]\begin{gathered} y=146(1+0.055)^x \\ y=146(1.055)^x \end{gathered}[/tex]4.
The initial value is 116
[tex]a=116[/tex]The growth rate is 117%
[tex]r=\frac{117}{100}=1.17[/tex]The equation is
[tex]\begin{gathered} y=116(1+1.17)^x \\ y=116(2.17)^x \end{gathered}[/tex]5.
The initial amount is 94
[tex]a=94[/tex]The decay rate is 13%
[tex]r=\frac{13}{100}=0.13[/tex]Since it is decay, then we will use (1 - r)
The equation is
[tex]\begin{gathered} y=94(1-0.13)^x \\ y=94(0.87)^x \end{gathered}[/tex]6.
The initial value is 142
[tex]a=142[/tex]The decay rate is 3%
[tex]r=\frac{3}{100}=0.03[/tex]The equation is
[tex]\begin{gathered} y=142(1-0.03)^x \\ y=142(0.97)^x \end{gathered}[/tex]7.
The initial value is 171
[tex]a=171[/tex]The decay rate is 0.3%
[tex]r=\frac{0.3}{100}=\frac{3}{1000}=0.003[/tex]The equation is
[tex]\begin{gathered} y=171(1-0.003)^x \\ y=171(0.997)^x \end{gathered}[/tex]