Question

function represents a linear or exponential function
each @3 points)
b.
exponential or linear? (circle one)
equation:____
on in a cave. the equation b(t)=60 - 2.5^{t} gives
in the context of this situation. (2 pts)

Explanation:

Step1: Calculate the differences of \(f(x)\) values

For \(x = 0\) to \(x = 1\): \(15−10 = 5\)
For \(x = 1\) to \(x = 2\): \(20−15 = 5\)
For \(x = 2\) to \(x = 3\): \(25−20 = 5\)
Since the differences are constant (\(5\)), it is a linear function.

Step2: Use the slope - intercept form \(y=mx + b\)

The slope \(m=\frac{\Delta y}{\Delta x}=\frac{5}{1}=5\)
When \(x = 0\), \(y=f(x)=10\), so the \(y\) - intercept \(b = 10\)
The equation is \(y = 5x+10\)

Answer:

Linear, \(y = 5x + 10\)