Question

learning goal from lesson 14.1 and 14.2 i can represent and interpret categorical and quantitative data based on two variables (independent and dependent). represent means: i can show two - variable data on a scatter plot. i can describe the relationship between the variables. i can identify a function of best fit for the data set. 10. the amount of bacteria in a fish tank was 830. after 5 hours, the amount of bacteria is 3202. complete the table to determine which of these equations could approximate the amount of bacteria. (lesson 14.1) (1 point) equation yes no b = 830(1.31)^h □ □ b = 3202(1.31)^h □ □ b = 830(3.86)^h □ □ b = 3202(3.86)^h □ □ 11. choose which sets of data can be modeled by an exponential function. (lesson 14.1) (1 point) table yes no x 1 2 3 4 y 3 6 9 12 □ □ x 1 2 3 4 y 1 5 25 125 □ □ x 1 2 3 4 y 108 36 12 4 □ □ x 1 2 3 4 y 2 4 8 16 □ □

Explanation:

Question 10 - Step1: Recall exponential - growth formula

The general form of an exponential - growth model is $b = b_0r^h$, where $b_0$ is the initial amount and $r$ is the growth factor and $h$ is the number of time - periods. The initial amount of bacteria $b_0 = 830$.

Question 10 - Step2: Substitute values

When $h = 5$, for $b = 830(1.31)^h$, we have $b=830\times(1.31)^5=830\times3.757695119\approx3200$ (close to 3202). For other equations, substituting $h = 0$ gives non - 830 initial values or incorrect growth when $h = 5$.

Question 11 - Step1: Recall the form of an exponential function

An exponential function has a constant ratio between consecutive $y$ values for a constant increase in $x$. For Table 1, $\frac{6}{3}=2$, $\frac{9}{6} = 1.5$, not a constant ratio, so not exponential.

Question 11 - Step2: Check ratios for Table 2

For Table 2, $\frac{5}{1}=5$, $\frac{25}{5}=5$, $\frac{125}{25}=5$, has a constant ratio of 5, so it is exponential.

Question 11 - Step3: Check ratios for Table 3

For Table 3, $\frac{36}{108}=\frac{1}{3}$, $\frac{12}{36}=\frac{1}{3}$, $\frac{4}{12}=\frac{1}{3}$, has a constant ratio of $\frac{1}{3}$, so it is exponential.

Question 11 - Step4: Check ratios for Table 4

For Table 4, $\frac{4}{2}=2$, $\frac{8}{4}=2$, $\frac{16}{8}=2$, has a constant ratio of 2, so it is exponential.

Answer:

Question 10:

b = 830(1.31)^h: Yes
b = 3202(1.31)^h: No
b = 830(3.86)^h: No
b = 3202(3.86)^h: No

Question 11:

Table 1 (x: 1, 2, 3, 4; y: 3, 6, 9, 12): No
Table 2 (x: 1, 2, 3, 4; y: 1, 5, 25, 125): Yes
Table 3 (x: 1, 2, 3, 4; y: 108, 36, 12, 4): Yes
Table 4 (x: 1, 2, 3, 4; y: 2, 4, 8, 16): Yes