Question

On January 1, 1990, 50 frogs are released at a lake that previously had no frogs. 12 years later, it is estimated that there are 12,000 frogs around the lake. Assume that the annual percentage increase in the frog population has been the same over this time period. Determine in which year there are one million frogs at the lake if the population continues to increase exponentially at the same rate.

162

likes
809 views

Answer to a math question On January 1, 1990, 50 frogs are released at a lake that previously had no frogs. 12 years later, it is estimated that there are 12,000 frogs around the lake. Assume that the annual percentage increase in the frog population has been the same over this time period. Determine in which year there are one million frogs at the lake if the population continues to increase exponentially at the same rate.

Expert avatar
Neal
4.5
56 Answers
Låt tillväxtekvationen modelleras som y\left(t\right)=50a^t där t är antalet år efter 1990 givet att y(0) = 50 och y(12) = 12000 y(12) = 12000 ger ekvationen som 50a^{12}=12000 \Rightarrow a^{12}=\frac{12000}{50} \Rightarrow a^{12}=240 \Rightarrow a=240^{\frac{1}{12}} Sätt y(t) = 1 miljon = 1000000 för att få ekvationen som 50\left(240\right)^{\frac{t}{12}}=1000000 \Rightarrow\left(240\right)^{\frac{t}{12}}=\frac{1000000}{50} \Rightarrow\left(240\right)^{\frac{t}{12}}=20000 Ta logaritmer med bas 10 på båda sidor för att få \frac{t}{12}\left(\log240\right)=\log20000 \Rightarrow t=\frac{12\times\log20000}{\log240} \Rightarrow t\approx\frac{12\times4.30103}{2.38021}\approx21.68 Obligatoriskt år = 1990 + 21,68 = 2011,68 = 2012 (avrundat till närmaste kalenderår) Svar: Ungefär år 2012 kommer det att finnas 1 miljon grodor.

Frequently asked questions (FAQs)
Question: Evaluate the integral of x^2 + 5x - 3 with respect to x, using the standard formulas of integrals.
+
What is the length of the hypotenuse in a right triangle with an angle of 35 degrees and an adjacent side of 7 meters?
+
What is the result of multiplying a vector with components (2, -3, 5) by a scalar of 4?
+
New questions in Mathematics
A=m/2-t isolate t
a to the power of 2 minus 16 over a plus 4, what is the result?
Convert the following function from standard form to vertex form f(x) = x^2 + 7x - 1
Y=-x^2-8x-15 X=-7
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
90 divided by 40
5 people can complete a task in 72 hours. How many people are needed to complete the task in 60 hours.
The ratio of tomatoes to red apples is 2:5. If there are 20 tomaoes in the garden, how many red apples are there?
1 plus 1
3(2•1+3)4
If you randomly selected one person from the 900 subjects in this study, what is the probability that the person exhibits the minimum BMI?
Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6
What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.
The market for economics textbooks is represented by the following supply and demand equations: P = 5 + 2Qs P = 20 - Qd Where P is the price in £s and Qs and Qd are the quantities supplied and demanded in thousands. What is the equilibrium price?
Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A drug is used to help prevent blood clots in certain patients. In clinical​ trials, among 4336 patients treated with the​ drug, 194 developed the adverse reaction of nausea. Construct a ​99% confidence interval for the proportion of adverse reactions.
What is the value of f(-3) for the function X squared+5x-8=
did an analysis of dropout from the nursing faculty at the Universidad Veracruzana. With a poblation of 122 students, it turned out that according to the gender data, the female sex predominates with 82%, and the male sex male is found with 12%. The main factors why students drop out are, first of all, "Not "re-enrolled" at 49%, second place "Personal reasons" at 20%, third place "change of school" in 11%, "lack of documents" and "economic reasons" in 7%, change of residence and lack of social service in 3%. Of this sample, how many students dropped out for other reasons?
15=5(x+3)
Let f(x)=-1/2x+5 evaluate f(-6)
f(r) = 1/r+9 find f(x^2) + 1