Question

exponential from two points (level 1)
question
write an exponential function in the form $y = ab^x$ that goes through the points $(0, 13)$ and $(5, 3159)$.
answer
attempt 1 out of 2

Explanation:

Step1: Find the value of \(a\) using the point \((0, 13)\)

Substitute \(x = 0\) and \(y = 13\) into the equation \(y = ab^x\).
We know that any non - zero number to the power of \(0\) is \(1\), so \(b^0=1\).
The equation becomes \(13=a\times b^{0}\), which simplifies to \(13 = a\times1\), so \(a = 13\).

Step2: Find the value of \(b\) using the point \((5, 3159)\) and \(a = 13\)

Substitute \(x = 5\), \(y = 3159\) and \(a = 13\) into the equation \(y=ab^{x}\).
We get \(3159 = 13\times b^{5}\).
First, divide both sides of the equation by \(13\): \(\frac{3159}{13}=b^{5}\).
Calculate \(\frac{3159}{13}=243\), so \(b^{5}=243\).
We know that \(3^{5}=243\), so \(b = 3\).

Step3: Write the exponential function

Now that we have \(a = 13\) and \(b = 3\), substitute these values into the form \(y = ab^{x}\).
The exponential function is \(y = 13\times3^{x}\).

Answer:

\(y = 13\cdot3^{x}\)