Waste less time on Facebook — follow Brilliant.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Exponential Functions
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
The population of a certain culture of bacteria at time \(t\) is given by \(P(t) = P_0 \times 10^{yt} \), where \(P_0\) is the initial amount of bacteria, \(y\) is the growth constant, and \(t\) is the time (in seconds). A scientist measures that the number of bacteria at time \(t=4\) is \(10^ {56}\) times the number of bacteria at time \(t=0\). Given this information, what is the growth constant \(y\) of this group of bacteria?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
\(pH\) measures the concentration of hydrogen ions \(H^+\) in a solution. Let \(pH=m\) if the number of gram ions of \(H^+\) in a \(1\)-liter solution is \(10^{-m}\).
Then the ratio of the number of gram ions of \(H^+\) for \(pH=6.5\) and the number of gram ions of \(H^+\) for \(pH=7.9\) can be expressed as \(10^a.\) What is the value of \(100a?\)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
The brightness of light is reduced by half when it penetrates a glass screen with \(11\) cm width. If the brightness of light has been reduced to \(12.50\) % of the initial brightness, how many glass screens with the same width did the light penetrate?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
If you invest \(1200\) dollars in savings account that pays \(4\) percents compound interest, then how long does it take to double your money?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
The number of particles in a given location after time \(t\) is modeled by the equation \(N(t) = N_0e^{-\frac{t}{21}}\). At what time \(t\) will the number of particles be equal to \(\frac{1}{e^3}\) of the initial number (when \(t=0\))?