A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence....
Bill and nine of his friends each have a lot of money in the bank. Bill has 10^10 dollars in his acc All nine of Bill's friends pooled together...
Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is a 1 followed by a googol of zeros. If each...
If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 10 times the sand as Beach A? (Express your...
1^10 = ? 1^10 = 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 1^10 = 1
9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this sequence? We see the following pattern in this...
3, 6, 12, 24, 48 What is the function machine for this sequence? We see the following pattern: 3 * 2^0 = 3 3 * 2^1 = 6 3 * 2^2 = 12 3 * 2^3 = 24...
1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence?...
10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term? We see the following pattern 10^1 = 10 10^3 = 1000 10^5 = 100,000 10^7 =...
1, 8, 27, 64 What is the 10th term? We see the following pattern: 1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 64 We build our sequence function using this...
2^n = 4^(n - 3) 2^n = (2^2)^(n - 3) (2^2)^(n - 3) = 2^2(n - 3) 2^n= 2^2(n - 3) Comparing exponents, we see that: n = 2(n - 3) n = 2n - 6...
5^(n - 1) = 15,625 We know 5^6 = 15,625, so we have: n - 1 = 6 Add 1 to each side: n - 1 + 1 = 6 + 1 Cancel the 1's on the left side: n = 7
if x^2=y^3, for what value of z does x^{3z}= y^9 y^9 = y^3 * y^3, so if we square the right side, we must square the left side for equivalence:...
raise b to the 6th power then find the sum of the result and 4 raise b to the 6th power b^6 raise b to the 6th power then find the sum of the...
3x to the power 2n We take the expression 3x raise it to the power of 2n (3x)^2n
The square of the difference of n and 2, increased by twice n The difference of n and 2: n - 2 The square of the difference of n and 2 means we...
c varies jointly as the square of q and cube of p The square of q means we raise q to the 2nd power: q^2 The cube of p means we raise p to the...
The cube of x is less than 15 The cube of x means we raise x to the 3rd power: x^3 Less than 15 means we setup the following inequality x^3 < 15
How many times bigger is 3^9 than 3^3 Using exponent rules, we see that: 3^9 = 3^3 * 3^6 So our answer is 3^6 times bigger
the square of the sum of 2a and 3b the sum of 2a and 3b 2a + 3b The square of this sum means we raise 2a + 3b to the 2nd power: (2a + 3b)^2
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