This function can be used to determine the number of bacteria in a culture h hours after the culture was started.

Question

f (h) = 10(3)^h

Which statement best describes the meaning of the equation f (2) = 90

A.
It gives the number of bacteria in the culture after 2 hours.

B.
It gives the number of bacteria in the culture after 3 hours.

C.
It gives the number of bacteria in the culture after 45 hours.

D.
It gives the number of bacteria in the culture after 90 hours.

Answer 1

To determine the meaning of the equation \( f(2) = 90 \) in the context of the function provided, we can start by evaluating the function at \( h = 2 \):

\[ f(2) = 10(3)^2 = 10 \times 9 = 90 \]

This tells us that there are 90 bacteria in the culture after 2 hours. Therefore, the correct statement is:

A. It gives the number of bacteria in the culture after 2 hours.

Answer 2

When Birchwood Elementrary School opened for the first year, there 240 students. During each of the following 10 years, the number of students increased exponentially. To determine the number of years (n) that had passed when the number of students reached 365, use the following function.

f (n) = 240(1.15)^n

After how many years did the number of students reach 365?

A.
1 year
B.
2 years
C.
3 years
D.
4 years

Answer 3

To determine how many years \( n \) it takes for the number of students to reach 365, we can set the function \( f(n) = 240(1.15)^n \) equal to 365 and solve for \( n \):

\[ 240(1.15)^n = 365 \]

Now, divide both sides by 240:

\[ (1.15)^n = \frac{365}{240} \]

Calculating the right side:

\[ \frac{365}{240} \approx 1.5208333 \]

Next, we take the logarithm of both sides to solve for \( n \):

\[ n \log(1.15) = \log(1.5208333) \]

Now, solving for \( n \):

\[ n = \frac{\log(1.5208333)}{\log(1.15)} \]

Calculating the logarithms:

\[ n \approx \frac{0.1828}{0.0672} \approx 2.72 \]

Since \( n \) must be a whole number, we round \( n \) to 3 years.

Thus, the number of years it takes for the number of students to reach 365 is approximately:

C. 3 years.

Answer 4

The height above the ground in feet of a ball kicked into the air from the balcony of an apartment is -16t^2 + 16t + 32, where t is the time in seconds since the ball was kicked. How high above the ground is the balcony?

A.
2 ft

B.
16 ft

C.
32 ft

D.
36 ft

Answer 5

To find the height above the ground from which the ball was kicked, we evaluate the function \( h(t) = -16t^2 + 16t + 32 \) at \( t = 0 \). This will give us the initial height of the ball, which corresponds to the height of the balcony.

Calculating:

\[ h(0) = -16(0)^2 + 16(0) + 32 = 32 \]

Thus, the height of the balcony above the ground is 32 feet.

So the correct answer is:

C. 32 ft.

Answer 6

A student wrote the inequality y > 4x - 17. Her friend solved the inequality and said that (12,31) is one of the possible solutions of this inequality.

A.
Yes, because 31 is equal to 4 * 12 - 17


B.
Yes, because 31 is greater than 4 * 12 - 17


C.
No, because 31 is equal to 4 * 12 - 17


D.
No, because 31 is less than 4 * 12 - 17

Answer 7

To determine if the point \((12, 31)\) is a solution to the inequality \(y > 4x - 17\), we can substitute \(x = 12\) into the inequality and see if \(y = 31\) satisfies it.

First, we calculate \(4 \cdot 12 - 17\):

\[ 4 \cdot 12 - 17 = 48 - 17 = 31 \]

Now, we need to compare \(y\) (which is 31) to \(4 \cdot 12 - 17\) (which is also 31):

The inequality \(y > 4x - 17\) translates to \(31 > 31\), which is false.

Since \(31\) is not greater than \(31\), \((12, 31)\) does not satisfy the inequality \(y > 4x - 17\).

Thus, the correct answer is:

C. No, because 31 is equal to 4 * 12 - 17.

Answer 8

Which ordered pair is on the graph of y = x^2 + 2 ?

(5, 49)

(4,10)

(-1,1)

(-6,38)

Answer 9

To determine which ordered pair is on the graph of the equation \(y = x^2 + 2\), we can substitute the \(x\)-value from each ordered pair into the equation and check if the resulting \(y\)-value matches the \(y\)-value in the ordered pair.

1. For (5, 49): \[ y = 5^2 + 2 = 25 + 2 = 27 \quad \text{(not 49)} \]

2. For (4, 10): \[ y = 4^2 + 2 = 16 + 2 = 18 \quad \text{(not 10)} \]

3. For (-1, 1): \[ y = (-1)^2 + 2 = 1 + 2 = 3 \quad \text{(not 1)} \]

4. For (-6, 38): \[ y = (-6)^2 + 2 = 36 + 2 = 38 \quad \text{(matches 38)} \]

The only ordered pair that lies on the graph of \(y = x^2 + 2\) is (-6, 38).

Answer 10

Joslyn is planting daisy seeds in a flower garden. Each day, she plants a different number of seeds. The list below shows the number of seeds Joslyn planted on each of the first six days.
1, 2, 4, 8, 16, 32

Joslyn wants to determine the number of daisy seeds, d, she should plant on the nth day. Which statements below are true? Select two that apply.

A.
The sequence is arithmetic.

B.
The sequence is geometric.

C.
The sequence is represented by d = 2n

D.
The sequence is represented by d = 2n - 1

E.
The sequence is represented by d = 2^n

F.
The sequence is represented by d = 2^n-1

Answer 11

To determine the correct statements about the sequence of daisy seeds planted by Joslyn, we first analyze the given numbers: \(1, 2, 4, 8, 16, 32\).

1. Observing the Structure of the Sequence:
   • Each number can be expressed as a power of 2:
     • \(1 = 2^0\)
     • \(2 = 2^1\)
     • \(4 = 2^2\)
     • \(8 = 2^3\)
     • \(16 = 2^4\)
     • \(32 = 2^5\)

From this, we can see that the sequence is based on powers of 2.

2. Identifying Properties:
   • Arithmetic Sequence: An arithmetic sequence has a constant difference between consecutive terms. In this sequence, the differences are not constant (e.g., \(2 - 1 = 1\), \(4 - 2 = 2\), \(8 - 4 = 4\), and so on). Therefore, A is false.
   • Geometric Sequence: A geometric sequence has a constant ratio between consecutive terms. In this case, each term is multiplied by \(2\) to get the next term, indicating that it is a geometric sequence. Therefore, B is true.
   • Expression for the Sequence:
     • d = 2n: This would imply that for the first day (n=1), d would be 2, which does not match our data (1). Therefore, C is false.
     • d = 2n - 1: For n=1, this gives 1 (correct), but it does not match all entries for n = 2 and beyond (e.g., for n=2, d = 3). Therefore, D is false.
     • d = 2^n: For n=1, this gives \(2^1 = 2\), which is incorrect as the first term of the sequence is 1. Therefore, E is false.
     • d = 2^n - 1: This means for n=1, \(2^1 - 1 = 1\), for n=2, \(2^2 - 1 = 3\) (wrong), but for n=3, \(2^3 - 1 = 7\). Incorrect yet validating. This statement is also misleading since it doesn't match other values properly occurring in the sequence. Therefore, F is false.

Thus, the only true statement is:

B. The sequence is geometric.

The other statements do not correctly represent the sequence as explored.

Therefore the correct solution is:

• B. The sequence is geometric.

(No other statements qualify as true among the options provided.)