MAT 117 UMBC Algebra Exponential Equations Problem Set

MAT 117Unit D Problem Set
1. [6 pts] Solve the exponential equations. Report your answers as fractions or integers.
a. 252𝑥+3 = 3125
b. 42𝑥−1 = 8𝑥+3
2. The spread of the Ebola virus in Africa in 2014 could be modeled by 𝐶(𝑡) = 188.59𝑒^(0.024𝑡)
where C(t) represents the number of cases, and t represents the number of days since May 1,
2014). (source: http://www.geert.io/exponential-growth-of-ebola.html)
a. [3 pts] Approximately how many cases were there on May 1, 2014 (round to two decimal
places)?
b. [3 pts] How many cases were projected by November 24, 2014 (round to 2 decimal places)?
c. [4 pts] Find C(92) and explain what it means in the context of the problem.
MAT 117
Unit D Problem Set
3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species,
environmentalists declared the insect endangered and transplanted the insect to protected
area. The population P(t) (in thousands) of insects in t months after being transplanted is 𝑃(𝑡) =
50∗(1+0.05𝑡)
2+0.01𝑡
a. [3 pts] Determine the number of months until the insect population reaches 40 thousand
(round to 2 decimal places).
b. [3 pts] What is the limiting factor on the insect population as time progresses? Explain your
answer.
c.
[3 pts] Sketch a graph of the function using the window 0 ≤ 𝑥 ≤ 700 and 0 ≤ 𝑦 ≤ 300. Be
sure to indicated the scale on the graph, label the axes, at least 2 points on the graph, and
any asymptotes.