Question

F(x)=7e^-2t growth or decay

Answer 1

`\bf a^{-{ n}} \implies \cfrac{1}{a^( n)}\qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \\ \quad \\\\ % negative exponential denominator a^{{ n}} \implies \cfrac{1}{a^(- n)} \qquad \qquad \cfrac{1}{a^(- n)}\implies \cfrac{1}{(1)/(a^( n))}\implies a^{{ n}} \\\\ -----------------------------\\\\ f(x)=7e^(-2t)\iff f(x)=7\cdot \cfrac{1}{e^(2t)}\iff f(x)=\cfrac{7}{e^(2t)}`


as "t" grows larger and larger, 10, 100, 10000, 1000000 and so on, the denominator becomes larger and larger, whilst the numerator is static, thus, the fraction becomes smaller and smaller

as "t" increases, f(x) decreases, decay