Upon landing on a newly discovered planet, Exponentia, astronauts discovered life. Scientists name the newly discovered creature
s Vietiens (vee-et-ee-ans), after the French mathematician Francois Viète, who helped develop exponents. In previous Units, you learned that the growth equation for an exponential function was f(t) = a(1 + r) t, where a represents the starting value of the population, r represents the growth rate as a decimal, and t represents time. 1. In 1999, the population of Vietiens was estimated at 1 million. Scientists have determined that the population grows at a rate of 10% per year a. Write an equation for the population of Exponentia as a function of years, t, since 1999. b. In 2005, how many years have passed since 1999? c. Use the function you created to determine the population of Vietiens in the year 2005. d. What will be the population of Vietiens in 2015? 2. a. Graph the function for the population of Exponentia in #1a on the interval 15 ( t ( 15. b. What are the domain and range of the entire function? Domain ___________________ Range ___________________ c. Explain why the domain and range in part b are not very realistic in this context. d. What are the asymptote(s) and intercept(s) for f(t)? Asymptote(s) ________________ Intercept(s) ______________ e. What, if anything, do the asymptote and intercepts mean in the context of the problem?
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We will have the following:
First, we construct the exponential decay function, that is:
Now, we will determine the population after 6 years:
So, the population after 6 years will be of approximately 37491 people-