Question

use the table to answer the question.

t	f(t)
1	950
2	900
3	850

which function represents f(t)?

a. $f(t) = -50t + 950$
b. $f(t) = -50t + 1000$
c. $f(t) = 50t + 950$
d. $f(t) = 50t + 1000$

Explanation:

Step1: Analyze the slope

The slope \( m \) of a linear function \( F(t)=mt + b \) is calculated as \( \frac{\Delta F(t)}{\Delta t} \). Using \( t = 0, F(t)=1000 \) and \( t = 1, F(t)=950 \), the slope \( m=\frac{950 - 1000}{1 - 0}=\frac{- 50}{1}=-50 \).

Step2: Find the y - intercept

The y - intercept \( b \) is the value of \( F(t) \) when \( t = 0 \). From the table, when \( t = 0 \), \( F(t)=1000 \), so \( b = 1000 \).

Step3: Form the function

Using the slope - intercept form \( F(t)=mt + b \) with \( m=-50 \) and \( b = 1000 \), we get \( F(t)=-50t + 1000 \). We can also verify by plugging in other values of \( t \) from the table. For \( t = 2 \), \( F(2)=-50\times2 + 1000=-100 + 1000 = 900 \) (which matches the table), and for \( t = 3 \), \( F(3)=-50\times3+1000=-150 + 1000 = 850 \) (which also matches the table).

Answer:

B. \( F(t)=-50t + 1000 \)