Applications of Exponential Functions
Exponential functions, a fundamental concept in mathematics, find wide-ranging applications across various fields. Their rapid growth or decay characteristics make them indispensable in modeling phenomena such as population growth, compound interest, radioactive decay, and epidemics. In finance, exponential functions govern compounding interest, influencing investment strategies and financial planning. In biology, these functions describe population growth dynamics, aiding in understanding ecosystems and species propagation. Additionally, in physics and engineering, exponential functions model processes like radioactive decay, electrical circuits, and signal amplification, contributing to technological advancements and scientific understanding. The versatility and ubiquity of exponential functions underscore their significance in diverse real-world applications.
- How do a construct an exponential equation given (0, -1) and (2, -36)?
- If the length of a side of a cube is 4x, what is the volume of the cube?
- What is the half-life of the substance if a sample of a radioactive substance decayed to 97.5% of its original amount after a year? (b) How long would it take the sample to decay to 80% of its original amount? _______years??
- How do you determine if the equation #y = 50(0.03)^x # represents exponential growth or decay?
- What is x if #log_2 (x+5) - log_2(x-2) +2= 3#?
- What is x if #log_2(x) + log_3(x + 1) = log_5(x - 4)#?
- Can you take the logarithm of a negative number?
- What is a natural log?
- How do you identify equations as exponential growth, exponential decay, linear growth or linear decay #f(x) = 9.6 ∙ 1.06x#?
- How many bird species will there be left in the year 2020 if in 1990, a rural area had 1200 bird species and are becoming extinct at the rate of 1.5% per decade (10 years)?
- What is the solution to the following system of equations?:# log6 + log(x-3) = 2logy, 2y - x = 3#
- How do you find the value of your investment after five year's growth if you invest $2000 in a bank offering 10% interest compounded weekly?
- Why is #3*ln(x) = ln(x^3)#?
- What is x if #lnx + ln5x^2 = 10#?
- Find the minimum value of #log_2^2 2 + log_ 2^3 2^2 + log_ 2^4 2^3.............log_2^n 2^(n-1)#?
- A firm producing positive amount gains by increasing its production. Whether it is true or false?
- The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. How do you write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years?
- How long will it take you to triple your money if you invest it at a rate 6% compounded annually?
- What are some Applications of Exponential Functions?
- How do you solve #5^x+1=625#?