PLEASE, I NEED YOU TO MAKE SURE THAT YOU ANSWERED ALL QUESTIONS CORRECTLY AND ENTIRELY.

KEEP IN MIND YOU ARE ONLY REQUIRED TO SHOW THE ENTIRE WORK FOR QUESTIONS 1,2,3,4 AND 5. AFTER THAT YOU DON'T HAVE TO SHOW WORK INSTEAD YOU CAN DIRECTLY PUT THE ANSWERS TO THE QUESTIONS.

ALL THE BOXES IN RED MEAN THAT MY PREVIOUS ANSWERS WERE NOT CORRECT SO YOU NEED TO FIX THEM.

1. Given the points (-1, 8) and (2, 1) determine the exponential function y = ab". 2. Graph the function f(x) = 2(3) and f(x) = 2 (3) on the grid below. -0- 6 -5 -4 -3 -2 -1 0 1- 2 3- -4- 5 6 x -3- 3. Abe opened a savings account and deposited $500 as principal. The account earns 6% interest, compounded continuously. What is the balance after 10 years?4. Take the exponential function at) = 3I and rewrite f (27)) in order to move the function 1 units to the right, 2 unit down and reect it over the maxis. 5. From the picture of the graph below, determine the exponential function. For each year, t, the population of a forest of trees, call it Forest A, is represented by the function A(t) = 115(1.025)t. In a neighboring forest, call it Forest B, the population of the same type of tree is represented by the function B(t) = 80(1.03)t. a. Which forest's population is growing at a faster rate? Select an answer a 5. Which forest had a greater number of trees initially? Select an answer 9 By how many (round to the nearest tree)? trees c. Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years (round to the nearest tree)? l Select an answer all By how many? trees The graph of f (9:) = 4m is reected about the y-axis and stretched vertically by a factor of 5. a. What is the equation of the new function, g(:c)? m = b. What is the yintercept? ( , ) c. What is the domain? 01. What is the range? a: 7 4 The graph of f(a:) = l (l) + 5 is shifted downards 5 units, and then shifted left 4 units, stretched 2 2 vertically by a factor of 4, and then reected about the as-axis. a. What is the equation of the new function, 9(33)? w b. What is the yintercept? ( , ) c. What is the domain? d. What is the range? The function f(x) - 5(2) is shown. Graph the reflection of f(x) about the x-axis on the same axes, and then give the horizontal asymptote, the domain and the range. 10 -9 8 -7 6 -54 3 4 5 6 7 8 9 7 Clear All Draw: Horizontal asymptote at y = o Domain: (-00,00) Preview Range: (0,-00) Preview (0, - 00).Start with the graph of f (as) = 5\". Then write a function that results from the given transformation. Shift f(a:) 5 units downward g(m>= . 51+1symaxok Start with the graph of f(x) = 8". Then write a function that results from the given transformation. Reflect f(x) about the y-axis g(2) = PreviewThe graph is a transformation of y = 2\". Write an equation that describes the transformation. q f(:c) = 2"x at 21 syntax 0k Evaluate the exponential function for the indicated value of x. Round your answer to 2 decimal places, if necessary. f(2) = =(2)2+3 for f(2) f ( 2) = 2~x+2Rewrite the equation in logarithmic form. 5 y The logarithmic form is log A (B) = C. Find A, B, and C. A = Preview B = Preview C = PreviewIs there a number a: such that In a: = 12? If so, what is the number? If not, enter "DNE". Preview State the domain, the vertical asymptote, and end behavior of the function. f(2) = 10g3(12 - 4ac) + 5 Domain: (-00,3) Preview Vertical asymptote at x = 3 Preview lim f(x) = 3 Preview OO lim f(x) = Preview x- 3Write a logarithmic equation corresponding to the graph shown. Use 3; = log a: as the parent function. 4