algebra 2b - unit 2: exam

examine the following logarithmic function f(x): f(x) = log x. match each part with its value.

x-intercept of f(x) : (1, 0) vertical asymptote of f(x) : x = 0 intersection of f(x) and the line y = 1 : (10, 1)

cara tracked the population of fish in a pond. at the end of the first year, she counted 8 fish. over the years, the population tripled each year. which equation can be used to determine the number of fish, f, after t years?

f = 8 * 3^(t-1)

the function f(x) is transformed to become g(x) = f(−2x). which statement correctly describes the transformation on f(x)?

f(x) is reflected across the y-axis and horizontally compressed by a factor of 1/2.

the function f(x) = log_3/4 x − 2 is translated to get g(x) = log_3/4 x + 4. what is the effect on f(x)?

f(x) moves 6 units upward.

the graph shows a translation of the preimage f(x) = log_3 x − 2 to become g(x). which is the transformation rule and the function rule for g(x)?

g(x) = f(x + 2) + 3 g(x) = log_3 (x + 2) + 1

examine the following function: h(x) = log_5 x which graph represents the function?

https://assets.learnosity.com/organisations/625/96797c9e-4f5f-4cf2-97df-408aaaec87c0.png

the town of swanford has a population of 12,500, but it is decreasing at a rate of 4% each year. which equation models the population of swanford, where p is the population after t years?

p = 12,500(0.96)^t

solve the equation for x. 3^6x+7 = 243

x = -1/3

solve the equation for x. 5 * 10^x+2 = 5000

x = 1

what is the value of log_4 62?

2.977

which interval represents all of the x-values where f(x) = log_13 x is positive?

0 < x < 1

match each logarithm with its equivalent expression.

ln 4^15 : 15 ln 4 log_m 15^4 : 4 log_m 15 log 4^m : m log 4

a sample of bacteria is grown in a petri dish. it contains 1,000 bacteria, and the population doubles every half hour. the inequality 1,000(2)^2t > 50,000, where t is the number of hours, models when the population of the bacteria sample will be greater than 50,000. based on the inequality, when will the population in the sample be greater than 50,000?

t > 3 hours

solve the equation for x. 5^4x-1 = 845

x = 1.297

carbon dating is used to determine the age of fossils. a fossil was found with 75% of the original carbon-14. the half-life of carbon-14 is 5,730 years. the equation that models the situation is 0.75 = (0.5)^ x/5,730. how old is the fossil?

x = 2,378

solve 7^2x-9 = 441 for x.

x = 6.065

solve the equation for x. 2^4x-3 = 2^x+18

x = 7

solve the equation for x. 4 * 3^x-2 = 60

x = log_3 15 + 2

if 3^x/5 = 24, what is the value of x?

x ≈ 14.464

examine the graph of the logarithmic function f(x). https://assets.learnosity.com/organisations/625/bce6b31f-2f50-4523-bbea-71b3a6a7599f.png match each part with its value.

x-intercept of f(x) : (1, 0) vertical asymptote of f(x) : x = 0 intersection of f(x) and the line y = 1 : (0.75, 1)