Modeling with Exponential and Logarithmic Equations Assignment 2

Radium-226, a common isotope of radium, has a half-life of 1,620 years. How many grams of a 120-gram sample will remain after t years? Which equation can you use to solve this problem?

C

Use logarithmic regression to find an equation of the form y = a + b ln(x) to model the data.

A= -76.204 B= 37.673

The loudness of a jack hammer is 96 dB. Its sound intensity is about The loudness of a compactor is 94 dB. Its sound intensity is about

0.004 0.0025

The sound intensity of the jack hammer is about times the sound intensity of the compactor.

1.6

After 100 years, about grams of the sample will remain.

115

The general equation for depreciation is given by y = A(1 - r)t, where y = current value, A = original cost, r = rate of depreciation, and t = time, in years. The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years? $

12,528.15

The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. What is the approximate pH of a solution if the concentration of hydrogen ions is 5.0 × 10-4 moles per liter?

3.3

The loudness of a pile driver is 112 dB. About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.

40

Using the graphing calculator, estimate to the nearest day how long it will take the corn to reach 6 feet tall: days

51 days

After 10 years, a $2,000-dollar investment compounded annually has grown to $3600. What is the interest rate to the nearest whole-number percent?

6%