Question 1(multiple choice worth 1 points)
(03.04 mc)
the population f(x), in millions, of state a of a country after x years is represented by the function shown below:
f(x) = 4(1.08)x
the graph shows the population g(x), in millions, of state b of the country after x years:
graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4
which conclusion is correct about the populations of state a and state b?
the original population of state a was double the original population of state b.
the original population of state b was double the original population of state a.
the original population of state a was four times the original population of state b.
the original population of state a was equal to the original population of state b.
question 2(multiple choice worth 1 points)
(03.02 lc)
the function f(x) = 3,267(1 + 0.02)x represents the amount of money in a savings account where x represents time in years. what does the 3,267 represent?
the amount of money in the savings account after one year
the amount of money added to the savings account each year
the initial amount of money placed in the savings account
the growth rate
question 3(multiple choice worth 1 points)
(03.03 lc)
given the exponential function f(x) = 16(0.75)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.
exponential growth, 75% increase
exponential decay, 75% decrease
exponential growth, 25% increase
exponential decay, 25% decrease
question 4(multiple choice worth 1 points)
(03.08 mc)
two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. use the data to determine which function is exponential, and use the table to justify your answer.
x f(x) g(x)
1995 $14,170.20 $11,008.31
2000 $19,396.20 $16,174.82
2005 $24,622.20 $23,766.11
2006 $25,667.40 $25,667.40
2007 $26,712.60 $27,720.79
2010 $31,938.60 $34,920.21
g(x) is exponential; an exponential function increases faster than a linear function.
g(x) is exponential; g(x) has a lower starting value and higher ending value.
f(x) is exponential; an exponential function increases more slowly than a linear function.
f(x) is exponential; f(x) increased less overall than g(x).
question 5(multiple choice worth 1 points)
(03.01 lc)
simplify the square root of 5 times the cube root of 5.
five to the five sixths power
five to the one sixth power
five to the two thirds power
five to the seven sixths power
question 6(multiple choice worth 1 points)
(03.03 mc)
the number of bacteria in a sample increased by a factor of 2 every minute from 9: 05 a. m. to 9: 55 a. m. the function below shows the number of bacteria in the sample f(x) after x minutes from 9: 05 a. m:
f(x) = 10(2)x
which of the following is a reasonable domain for the function?
0 ≤ x ≤ 10
5 ≤ x ≤ 55
0 ≤ x ≤ 50
all positive integers
question 7(multiple choice worth 1 points)
(03.02 mc)
initially, there were only 86 weeds in the garden. the weeds grew at a rate of 18% each week. the following function represents the weekly weed growth: f(x) = 86(1.18)x. rewrite the function to show how quickly the weeds grow each day.
f(x) = 86(1.02)x; grows approximately at a rate of 0.2% daily
f(x) = 86(1.18)7x; grows approximately at a rate of 1.8% daily
f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily
f(x) = 86(1.187)x; grows approximately at a rate of 0.18% daily
question 8(multiple choice worth 1 points)
(03.01 mc)
an expression is shown below:
the square root of 18 plus the square root of 2
which statement is true about the expression?
it is rational and equal to 4 times the square root of 2.
it is irrational and equal to 4 times the square root of 2.
it is rational and equal to 3 times the square root of 2.
it is irrational and equal to 3 times the square root of 2.