Sophia College Algebra milestone 5 Final

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In the general exponential equation , the value will give us the location of the yintercept. Since , we know that the correct graph will have a y-intercept at a a equals short dash 2 left parenthesis 0 comma short dash 2 right parenthesis 1/4/2021 Sophia :: Welcome https://phoenix.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7392181 5/24 . Next, we can determine the end behavior of the graph by looking at the sign of . When the value is negative, while approaches positive infinity, approaches negative infinity. It's decreasing instead of increasing. Also, while approaches negative infinity, approaches 0 as they were with a graph of our equation with a positive value. This is the correct graph of because it has a yintercept at and shows going from 0 to negative infinity as you read the graph from left to right. a x y x y open parentheses 0 comma short dash 2 close parentheses y 1/4/2021 Sophia :: Welcome https://phoenix.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7392181 6/24 CONCEPT Graph of an Exponential Equation 2 Find the solution to the following equation. 1/4/2021 Sophia :: Welcome https://phoenix.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7392181 7/24 RATIONALE To solve this equation, first re-write the term on the right side so that both terms have a common base. Since is a power of , we can re-write as . The two terms now have the same base, . Use the properties of exponents to simplify by multiplying the exponents and . times is equal to . Because the bases are the same, we can focus on the exponents and set them equal to each other. Since the exponents are equivalent, we can simply solve for . Add to both sides to undo the on the right. We now have the term isolated on the left side. Next, divide both sides by to solve for x. Once we divide by , we have isolated x on the left side. However, we can still simplify this fraction. is equivalent to . The solution for x is . CONCEPT Solving an Exponential Equation 3 Suppose $40,000 is deposited into an account paying 2.5% interest, compounded continuously. How much money is in the account after eight years if no withdrawals or additional deposits are made?

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