Question

A.Find the values for j and k

B.Write an equation for f(x)

Answer 1

well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

`{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^(2+3)\implies 9375=ab^2 b^3`

`\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}`

a)

`\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875`