SAT MATH PRACTICE QUESTIONS EXPONENTIAL EQUATIONS

Problem 1 :

If a and b are positive integers and 5^{a + b} = 5^3c, which of the following is equal to 5^9c ?

a)  5^{3a + b}      b) 15^{a + b}        c) 25^{3a + 3b}        d)  125^{a + b}   

 e) 125^{3a + 3b}

Solution

Problem 2 :

(x² y³)^1/2 (x² y³)^1/3 = x^a/3  y^a/2

If the equation above, where a is constant is true for all positive values of x and y, what is the value of a ?

a)  2      b)  3      c)  5      d)  6

Solution

Problem 3 :

If 49 = (7y)² then y could equal which of the following 

I   -1       II     1     III   7

a)  II only     b)  III only      c)  I and II      d)  I and III 

d)  II and III

Solution

Problem 4 :

If (a⁶ a⁶)^k = (a³)^{k + 5} , where a is a constant greater than 1, what is the value of k ?

a)  3/2      b)  5/3     c)  2       d)  3     e)  5

Solution

Problem 5 :

If t and w are positive numbers and t⁸ / t² = w¹², then

w⁸ / w²

a)  t²      b)  t³       c)  t⁴        d)  t⁶       e)  t¹²

Solution

Problem 6 :

If t > 0 and t² − 4 = 0 , what is the value of t ?

Solution

Problem 7 :

If a²  = 4, then a⁶ = 

a)  12      b)  16       c)  24        d)  32       e)  64

Solution

Problem 8 :

k^ (x² + xy) k^ (y² + xy) = k²⁵

In the equation above, k > 1 and x = 3 what is the positive value of y ?

a)  1      b)  2       c)  4        d)  5

Solution

Problem 9 :

If 3x - y = 12, what is the value of 8^x/2^y ?

a)  2¹²      b)  44       c)  82 

d) The value cannot be determined from the information given

Solution

Problem 10 :

25^x/5^x+3 = (1/125)^{x + 1}

Solution

Problem 1 :

The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table.

Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks?

a) Increasing linear      b) Decreasing linear

c) Exponential growth     d) Exponential decay

Solution

Problem 2 :

f (x) = 2^x + 1

The function f is defined by the equation above. Which of the following is the graph of y = −f(x) in the xy-plane?

Solution

Problem 3 :

Which of the following equations relates y to x for the values in the table above?

Solution

Problem 4 :

The world’s population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world’s population P, in billions of people, t years since 1975 ? (1 billion = 1,000,000,000)

a) P(t) = 4 (1.019)^t       b) P(t) = 4 (1.9)^t

c) P(t) = 1.19t + 4       d) P(t) = 1.019t + 4

Solution

Problem 5 :

P(t) = 60(3)^t/2

The number of microscopic organisms in a petri dish grows exponentially with time. The function P above models the number of organisms after growing for t days. Based on the function which of the following statements is true ?

a) The predicted number of organisms in the dish triples every two days.

b)  The predicted number of organisms in the dish doubles  every three days.

c)  The predicted number of organisms in the dish triples every day

d)  The predicted number of organisms in the dish doubles  every two day.

Solution

Problem 6 :

P = 2000x

P = 500 (2)^x

A website administrator is considering using one of the two models above to predict the total number of purchases. P made x weeks after the website advertising campaign begins. How many more purchases are predicted by the exponential model than the linear model 5 weeks after the advertising campaign begins ? 

a)  6000        b)  8000    c)  10000    d) 18000

Solution

Problem 7 :

If p percent of an adult's daily allowance of potassium is provided by x servings of Crunchy Grain cereal per day, which of the following expresses p in terms of x ?

a) p = 0.5x        b)  p = 5x       c)  p = (0.05)^x   

d) p = (1.05)^x 

Solution