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Exponential Growth Model Algebra Examples

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1. The population of a city was 124 thousand in 1992. The exponential growth rate was 1.6% per year. Use the exponential growth model p0e^kt.
a) Find the exponential growth function in terms of t, where t is the number of years since 1992.
p(t)=

2. The length of the instruction book for a country's tax code increased exponentially from 5 pages in 1935 to 163 pages in 2011.

a) Let t=0 correspond to 1935 and t=76 correspond to 2011. Then t is the number of years since 1935. Use the data points (0,5) and (76,163) to find the exponential growth rate and fit an exponential growth function C(t)=C0ekt to the data, where C(t) is the number of pages in the instruction book.

b) Use the function found in part (a) to estimate the total number of pages in the instruction book in 2013.

c) When will there be 625 pages in the instruction book?
a) C(t)=
(Type your answer using exponential notation. Use integers or decimals for any numbers in the equation. Do not round until the final answer. Then round to the nearest thousandth as needed.)

3. The sales, S, of a product have declined in recent years. There were 203 million sold in 1984 and 1.3 million sold in 1994. Assume the sales are decreasing according to the exponential decay model, S(t)=S0e−kt.
a) Find the value k and write an exponential function that describes the number sold after time, t, in years since 1984.
b) Estimate the sales of the product in the year 2002.
c) In what year (theoretically) will only 1 of the product be sold?  
a) Rounded to six decimal places, k=

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Solution Summary

This solution consists of examples of solving exponential growth models.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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