Understanding Exponential and Logarithmic Functions: Unit Test
School
Online High School**We aren't endorsed by this school
Course
SCIENCE 23848
Subject
Statistics
Date
Dec 11, 2024
Pages
2
Uploaded by DeaconSummer15912
Name:Date:Graded AssignmentUnit Test, Part 2: Exponential and Logarithmic FunctionsAnswer the questions below. When you are finished, submit this test to your teacher for full credit.Total score: ____ of 15 points(Score for Question 1: ___ of 5 points)1.The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually.(a)Use the exponential growth model to write an equation that estimates the population t years after 2010.(a)Estimate the population of the town in 2022. Show your work.Answer: the estimated population of the town in 2022 is 6689(Score for Question 2: ___ of 5 points)2.The formula determines the magnitude of an earthquake, where I is the intensity of the earthquake and S is the intensity of a “standard earthquake.” How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work.Answer:8 = log I^8 / S becomes I^8 = s * 10 ^ 86 = log I^8 / I^6 = S * 10^8 / S * 10^6 = 10^2 = 100a earthquake with a magnitude of 8 is 100 times stronger than a earthquake with a magnitude of 6
(Score for Question 3: ___ of 5 points)3.A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a)Write an equation to represent the amount of money in the account as a function of time in years.(b)Find the amount of time it takes for the account balance to reach $800. Show your work. Answer:800 = 500 * (1.015)divide both by 5001.6 = (1.015) t In (1.6) = t * In (1.015) t= In (1.6) ----------In (1.015) it will take near 31.57 years for the balance to reach 800