**2) Exponential Function Problem:**Write a formula for an exponential function with an initial value of 700 that decreases at a fixed percentage rate of 6.4% per unit time. Provide a brief explanation of your thinking.**Solution:**An exponential function that models decay can be written as:\[ f(t) = a \cdot (1 - r)^t \]where:- $ a $ is the initial value,- $ r $ is the rate of decay (as a decimal),- $ t $ is the time.For this problem:- Initial value $ a = 700 $,- Rate of decay $ r = 0.064 $.Thus, the formula is:\[ f(t) = 700 \cdot (1 - 0.064)^t = 700 \cdot 0.936^t \]**3) Linear Function Problem:**Suppose $ f(x) = \frac{2x + 7}{3} $. Determine the formula for a linear function that is perpendicular to $ f(x) $ and goes through the point (47, -115). Provide a brief explanation of your thinking.**Solution:**The slope ($ m $) of a linear function $ f(x) = \frac{2}{3}x + \frac{7}{3} $.To find a perpendicular line, use the negative reciprocal of the slope:- Slope of the perpendicular line = $-\frac{3}{2}$.To find the equation of the line, use the point-slope form:\[ y - y_1 = m(x - x_1) \]Using the point $ (47, -115) $:\[ y + 115 = -\frac{3}{2}(x - 47) \]Simplifying:\[ y = -\frac{3}{2}x + \frac{3}{2} \cdot 47 - 115 \]\[ y = -\frac{3}{2}x + 70.5 - 115 \]\[ y = -\frac{3}{2}x - 44.5 \]Thus, the equation of the linear function is:\[ y = -\frac{3}{2}x + 44.5 \]

Answered: 2) Write a formula for an exponential…

2) Write a formula for an exponential function with an initial value of 700 that decreases at a fixed percentage rate of 6.4% per unit time. Provide a brief explanation of your thinking.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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