University:
Morehouse College
Course:
HMTH 105 | College Algebra 1
Academic year:

2024
Views:

392

Pages:

4
Author:

Reynaldo Wong

Question 1 Find a recursive rule that models the exponential growth ! y = 1800 * (1.11) ^ t Answer 1 The functional form the given equation can be written as f(t) = 1800 * (1.11) ^ t * v f(0) = 1800o 1.11 is the ratio of successive values of the That is (f(1))/(f(0)) = (f(2))/(f(1)) =...= f(t+1) f(t) =...=1.11 So the recursive rule for this function van be written as f(t + 1) = 1.11f(t) Question 2 Transform the given differential equation or system into an equivalent system of first- order differential equations. x^ prime prime + 2 * x' + 26x = 82cos 4t Answer 1 Transform the given differential equation or system into an equivalent system of first- order differential equations. r^ prime prime + 2 * x' + 26x = 87 4t The second-order equation x^ prime prime + 2 * x' + 26x = 82cos 4t is equivalent to system f(t, x, x') = 82cos 4t - 26x - 2 * x' Hense the substitutions z₁=2,22=2=2 yield the system 82cos4t-2621-22 is a system of first-order equation. Question 3 Sketch a graph of the function. Use transformations of functions whenever possible. () Answer 1 Step 1 First graph function y z Then, to obtain graph of function f(z)z, do following transformations: -reflect with respect to x-axis On graph: Red-y Blue-f(x)=-2 Step 2 Question 4 Sketch a graph of the function. Use transformations of functions whenever possible. f(x) = 1/3 * (x - 5), 2 <= x <= 8 Answer 1 We need to graph the given function f(x) = 1/3 * (x - 5) for the restricted domain of 2<<& Since f(x) is linear, we can by finding its endpoints at x = 2 and & and then connecting the two points with a segment. Evaluating f(x) at x = 2 and -8 gives f(2) = 1/(3/1) * (2 - 5) = 1 3 1 (-3)=-1 f(8) = 1/3 * (8 - 5) = 1/3 * (3) = 1 To graph f(x), you can then plot the endpoints of (2-1) and (8.1) and then connect them with a segment: Question 5 The values of two functions, f and a, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are. 2 101 2 f(x) 31.5 10.5 3.5 10.5 31.5 g(x) 0.2 0.6 1.8 5.4 10.8 Answer 1 Consider the table of f(x) -2-10 1 f(z) 31.5 10.5 3.5 10.5 31.5 2 g(x) 0.2 0.6 1.8 5.4 10.8 The difference of f(x) is given as 10.531.5-20 3.5-10.5-7 10.5-3.5-7 31.5 10.5-20 Thus, the function f(x) is not growing exponentially and thus exponential function for f(x) doesn't exist 9(2) 0.2 0.6 1.8 5.4 10.8 as we can that g(x) has same multiplier as 3 common ratio 0.6 3 Hence f(x)=DNE Consider the table of g(x) 2-10 12 0.6 3 1.8 3 10.83 5.4 Hence common ratio b=3 and initial value is a=1.8 Hence, g(z) 1.8(3)