Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 21
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 • Q12 • Q13 • Q14 • Q15 • Q16 • Q17 • Q18 • Q19 • Q20 • Q21 • Q22 • Q23 • Q24 • Q25 • Q26 • Q27(a) • Q27(b) • Q27(c) • Q28(a) • Q28(b) • Q29(a) • Q29(b) • Q30 •
Question 21 

Which of the following is a solution to the differential equation with initial condition ? Select all that apply. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The initial condition tells us that the derivative , which is a positive number. What does this mean in terms of the growth of the function ? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The initial condition rules out the topleft, topright and bottomcentre graphs. The fact that the slope of the tangent line at is rules out the topcentre and bottomleft graphs, which have tangent lines of slope , so only the bottomright graph can be a solution of the differential equation. Alternatively, the solutions of are of the form , where is a constant. In this case, the solution is , and we can use this function to rule out all of the graphs, save for the bottomright one. 