Problem
MAT100-30 COLLEGE ALGEBRA 2023-2 $\leftarrow 11.01$ - Linear Function Ap... CURRENT OBJECTIVE Represent a real-world application as a linear function Question The population in a certain town is increasing linearly each year. The population at time $t=3$ is 1285 and at time $t=8$ is 2460 , where $t$ is the number of years after 1990. If $P(t)$ is the population at time $t$, write the equation below that correctly represents this situation. Provide your answer below: \[ P(t)= \] FEEDBACK MORE INSTRUCTION SUBMIT Content attribution
Solution
Step 1 ：Looking at the given data, we see that increasing $t$ by five results in an increase in $P(t)$ of $1175$. Thus for every increase in $t$ of $1$, $P(t)$ increases by $\frac{1175}{5}=235$.
Step 2 ：If $t = 3$ gives $P(t) = 1285$, then $t = t$ gives $P(t) = 1285 + (t-3)\cdot 235$.
Step 3 ：So the equation that correctly represents this situation is $P(t) = 1285 + (t-3)\cdot 235$.
Step 4 ：Simplify the equation, we get $P(t) = \boxed{235t + 435}$.
