1. (5x) ⁴ = x x = (5x5x5x5) x = 625 b. a³x a¹ ⁷ x a ² =a²² c. m = 7 - (-3) m = 10 x 3 m = 30 d. a 0 b7 c-3 = 2b ⁵ c ³ 2b5 c3 a b ⁷ c ³ e. (m)12 (m)3 (n) _ = (n) (n) 9 (n)3 (m) (m) 2. a. 7 - 3 = 4 4 ÷ 2 = 2 2 (1) ⁴ 2 (3) = 81 b. -4 + 2 = -2 _1 (5)2 (6) (5)2 = 25 (6) 36 36 25 c. 1 (1)3 (7) (1)3 = 1_ (7) 343 d. (1.4) ¹ ⁵ = 1.4 ⁷ (1.4) ⁸ (1.4) ² x (1.4) ⁷ = 20.66 e. (17 ⁹ x 17- ⁶ ) ⁴ = 83521 17 ⁸ 3. 4 ⁴ + 3 - 7 = 4x ⁴ -4 = 3(x+4) x 2-7 3 x 2 = 6 = 6(x+4)-7 =6x+24-7 =6x+17 4. (2x ² - 8x - 42) = 4x -8 =2(x ² -4x -21) =2(x+3)(x-7) 5. I = 1500 x (1.028) ¹ ⁰ I = $1977 over 10 years 6. Table a Linear x 0 1 2 3 4 5 y 2 7 12 17 22 27 5 5 5 5 5 The difference in y is a constant, 5. Slope = 5 The equation for linear combinations is y = mx + b y= 5x + 2 y= d = 5x+2 dx = (-2, 0) 5 Roots at -0.4 y-axis intercept at (0|2) Table b Exponential x 0 1 2 3 4 5 y 3 6 12 24 48 96 3 6 12 24 48 The table follows a pattern on the y axis. It is rising rapidly by the next term and is verified at right The formula for exponential relations is f(x) = ab^x This forms the equation: f(x) = 3(3) x Which is equal to: a= 3 b= 3 6/3 = 2 y = 3(2) Table 3 Quadratic x 0 1 2 3 4 5 y 5 3 5 11 21 35 2 -2 2 6 10 14 4 4 4 4 The first difference is not constant but the second one is f(x) = ax The formula for quadratic relations is ax^{2}+bx+c=0 Which forms the equation y= 4x ² + 5x + 5 7. 7. A polynomial function is an equation formed with the use of variables, exponents, and coefficients together using whole number exponents. It can have different exponents and is formatted with operations and equal signs. An equation for this function would be x^2 - 3x + 2 = 0 while the function would add the variables f(x) to the equation to complete the equation Exponential functions are equations which use x as the base and exponent An example of this would be the equation f(x) = ab^x, which utilizes the x function in both bases 8. An asymptote is a line that follows an infinitely long length as part of a rise of decline. It approaches the curve of a line but never meets it. Asymptotes will typically look like this on a graph 9. Appreciation is the rise of value in an asset, where the graph goes upward indicating an increase. Depreciation is the fall of a graph indicating a decrease in value. Example 10. The curve of the equation gradually moves upwards towards the y axis It is moved by 3.5 units upwards, 1.5 units to the left The ^2 exponent becomes the secondary point on the upper axis while the x and y =values have been moved to curve directly on the centre, making a position of (0,0) for both x and y. 11. a) -2(x-1) ² + 5 = 7 The max height reached in this curve is a distance of 7 meters b) 5 m c) t = -1 +( 1) ² - 4(-2)(5) 2( 2) t = -1 + (1) + (40) 4 t= -1 + 1 √40 4 t= 6.32 4 t= 1.58 seconds D. 3m 12. Both intercept at 1, both go on infinitely, and both have no defined starting point On the contrary, intercepts from the negative x axis while the other intercepts from the positive, the negative line rises slightly slower than the fast one 13. One month = 30/3 = 10 Half = 0.5 0.5 10 = 0.0009766 = 450 g x 0.0009766 = 0.439 g = 0.44 g 0.44 14. C = 900(1+0.08) Over 2 years C = 900(1+0.08) 900(1+0.08) c= 900(1+0.08) 25 c= $6163.62