$遞增型\; f(x)=k\cdot a^x $

$ =x\left[\left (log\;3+log\;7 \right )-\left( log\;100-log\;5  \right)  \right]$

$ =x\left( 3\;log\;3-2\;log\;5  \right)  $

$ =x\left( log\;3^2-log\;2^3  \right)  $

$ =x\left( 0.4771+0.8451-2+0.6990  \right)  $

$ =0.0212\;x $

$ =x\left( 3\times 0.4771-2\times 0.6990  \right)  $

$ =0.0333\;x $

$ =x\left( 2\times0.4771-3\times0.3010  \right)  $

$ =0.0512\;x $

Next

Reset

n = 9 (slider from 2 to 9, step 1)
list1: {5, 8, 12.5}
k = 3 (slider from 1 to 3, step 1)
b = Element(list1, k)
list2: {1.05, 1.08, 1.125}
text03: "$ ⇒" + (LaTeX[n]) + "=\left(    " + (LaTeX[FractionText[Element[list2, k]]]) + "\right)^x $"
list3: {"", "0.3010", "0.4771", "0.6020", "0.6990", "0.7781", "0.8451", "0.9030", "0.9542"}
text06: "$ ⇒" + (LaTeX[Element[list3, n]]) + " =x\left( log\;" + (LaTeX[If[k ≟ 1, 21, If[k ≟ 2, 27, 9]]]) + "-log\;" + (LaTeX[If[k ≟ 1, 20, If[k ≟ 2, 25, 8]]]) + "  \right) $"
list4: {0, 0.301, 0.4771, 0.602, 0.699, 0.7781, 0.8451, 0.903, 0.9542}
list5: {0.0212, 0.0333, 0.0512}
step = 0 (slider from 0 to 11, step 1)
text11: "$ ⇒x= " + (LaTeX[floor(Element[list4, n] / Element[list5, k]) + 1]) + "$"
t_Q: "$ 設臺灣地區國民生產毛額為\;a \;億元，\;若每年平均成長\;" + (LaTeX[b]) + "%，\;則經過幾年後變為\;" + (LaTeX[n]) + "\;倍？$
$Sol：$"
text02: "$ " + (LaTeX[n]) + "a=a(1+" + (LaTeX[b]) + "%) ^x$"
text04: "$ ⇒log\;" + (LaTeX[n]) + "=log\left( " + (LaTeX[FractionText[Element[list2, k]]]) + "  \right) ^x $"
text05: "=x\cdot log" + (LaTeX[FractionText[Element[list2, k]]]) + ""
A = Corner(4)
text01: "假設\;x\;年後國民生產毛額變為" + (LaTeX[n]) + "倍"
text10_1: "$ ⇒x=\frac{" + (LaTeX[Element[list3, n]]) + "}{" + (LaTeX[If[k ≟ 1, "0.0212", If[k ≟ 2, "0.0333", "0.0512"]]]) + "} =" + (LaTeX[Element[list4, n] / Element[list5, k]]) + "$"