# 1. Students in a fifth-grade class were given an exam. During the next 2 years, the same students...

## Question:

1. Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model {eq}f(t) =94?14log10(t+1), 0 \leq t \leq 24 {/eq} where {eq}t {/eq} is the time in months.

After how many months would it take for it to predict that the average dropped to {eq}90 {/eq}? (Assume that the the model could continue past two years, if necessary)

2.Oil leaks from a tank. At hour {eq}t=0 {/eq} there are {eq}200 {/eq} gallons of oil in the tank. Each hour after that, {eq}6\% {/eq} of the oil leaks out.

(a) What percent of the original {eq}200 {/eq} gallons has leaked out after {eq}12 {/eq} hours?

(b) If {eq}Q(t)=Q0e^kt {/eq} is the quantity of oil remaining after t hours, find the value of {eq}k {/eq}.

## Constructing and Solving Differential equations:

This problem involves constructing a first-order differential equation based on the given conditions in the problem statement. Then we solve this differential equation using the given boundary condition to find the value of the function at some specific point in time.

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1) Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was...

First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.