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Home Question Bank Math Pre Calculus Archive 2025 January 28

Pre-calculus Questions from Jan 28,2025

Browse the Pre-calculus Q&A Archive for Jan 28,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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QUESTION 3 A geometric series has a constant ratio of \( \frac{1}{2} \) and a sum to infinity of 6 . \( 3.1 \quad \) Calculate the first term of the series. \( 3.2 \quad \) Calculate the \( 8^{\text {th }} \) term of the series. \( \begin{array}{ll}3.3 & \text { Given: } \sum_{k=1}^{n} 3(2)^{1-k}=5,8125 \quad \text { Calculate the value of } n . \\ 3.4 & \text { If } \sum_{k=1}^{20} 3(2)^{1-k}=p \text {, write down } \sum_{k=1}^{20} 24(2)^{-k} \text { in terms of } p .\end{array} \) Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1900 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2003? 242216488 (Note: once diseases become widespread, they start to behave more like logistic growth, but don't worry about that for the purpose of this exercise) Question Help: Video Determine whether the function is even, odd, or neither. Then determine whether the function's graph \( f(x)=x \sqrt{4-x^{2}} \) Determine whether the function is even, odd, or neither. Choose the correct answer below. even neither odd Determine whether the graph of the function is symmetric with respect to the \( y \)-axis, the origin, or nei y-axis origin neither Determine whether the function is even, odd, or neither. Then determine whether the fi \( f(x)=x \sqrt{4-x^{2}} \) Determine whether the function is even, odd, or neither. Choose the correct answer be even neither odd (b) For a certain series, it is given that \( \sum_{i=1} T_{i}=5 n^{2}-2 n \). (1) Calculate the sum of the first 50 terms of the series. (2) Determine \( T_{20} \). (3) How many terms of the series will add up to 6055 ? (c) The sum to \( n \) terms of a series is given by \( S_{n}=\frac{n}{2}[8 n-7] \). (1) How many terms must be added to get a sum of 9825 ? Determine whether each function represents exponential growth or exponential decay. \( m(t)=\left(\frac{4}{5}\right)^{t} \) [Select ] Determine whether each function represents exponential growth or exponential decay. \( r(t)=0.4(1.06)^{t} \) [Select ] Determine whether each function represents exponential growth or exponential decay \( g(t)=2\left(\frac{5}{4}\right)^{x} \) [Select ] \( y = \operatorname { arcsen } ^ { 2 } \frac { 2 + x } { 3 } \) Applications of Logarithmic Functions Just as seismologists use magnitude to measure the intensity of earthquakes, physicists use decibels (notated by dB ) to measure the intensity of sound. The formula for the number of decibels is given by \( \mathrm{dB}=10 \log _{10}\left(\frac{I}{I_{0}}\right) \), where \( I \) is the intensity of the sound and \( I_{0} \) is the intensity of the quietest sound the average human ear can hear. 1. How many decibels is the quietest sound the average human ear can hear? In other words, what happens when we use \( I=I_{0} \) in the equation for decibels?
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