Question

Use the table to answer the question.

This table tracks the number of beetles (350) over time as it increases at a rate of 25% per month, modeled by an exponential equation.
x | f(x)
0 | 350
1 | [?]
2 | [?]
3 | [?]
4 | [?]
5 | [?]
A certain population of beetles is increasing at a rate of 22% per month. If there are currently 350 beetles, the equation f(x)=350(1.22)^x
can be used to model the situation. Finish the chart and plot the points to determine which graph correctly displays the situation.(1 point)

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
▼Click for Long Desc
The approximate coordinates of the curve are as follows: left parenthesis 0 comma 350 right parenthesis, left parenthesis 1 comma 270 right parenthesis, left parenthesis 2 comma 220 right parenthesis, left parenthesis 3 comma 170 right parenthesis, left parenthesis 4 comma 130 right parenthesis, left parenthesis 5 comma 100 right parenthesis, left parenthesis 6 comma 75 right parenthesis, left parenthesis 7 comma 65 right parenthesis, left parenthesis 8 comma 50 right parenthesis, left parenthesis 9 comma 40 right parenthesis, and left parenthesis 10 comma 30 right parenthesis.

An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
▼Click for Long Desc
The approximate coordinates of the curve are as follows: left parenthesis 380 comma 0 right parenthesis, left parenthesis 800 comma 4.1 right parenthesis, left parenthesis 1200 comma 6.2 right parenthesis, left parenthesis 1400 comma 7 right parenthesis, left parenthesis 1600 comma 7.6 right parenthesis, left parenthesis 1700 comma 8.2 right parenthesis, and left parenthesis 2000 comma 8.8 right parenthesis.

An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.
▼Click for Long Desc
The approximate coordinates of the curve are as follows: left parenthesis 0 comma 350 right parenthesis, left parenthesis 2 comma 525 right parenthesis, left parenthesis 3 comma 600 right parenthesis, left parenthesis 4 comma 775 right parenthesis, left parenthesis 5 comma 900 right parenthesis, left parenthesis 6 comma 1150 right parenthesis, left parenthesis 7 comma 1350 right parenthesis, left parenthesis 8 comma 1700 right parenthesis, and left parenthesis 8.8 comma 2000 right parenthesis.

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
▼Click for Long Desc
The approximate coordinates for the curve are as follows: left parenthesis 0 comma 350 right parenthesis, left parenthesis 1 comma 75 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 3 comma 5 right parenthesis, left parenthesis 4 comma 0 right parenthesis, left parenthesis 5 comma 0 right parenthesis, left parenthesis 6 comma 0 right parenthesis, left parenthesis 7 comma 0 right parenthesis, left parenthesis 8 comma 0 right parenthesis, left parenthesis 9 comma 0 right parenthesis, and left parenthesis 10 comma 0 right parenthesis.

Answer 1

Using f(x) = 350(1.22)^x (22% growth):

x = 0: 350
x = 1: 350(1.22) = 427
x = 2: 350(1.22)^2 ≈ 520.94 → 521
x = 3: 350(1.22)^3 ≈ 635.55 → 636
x = 4: 350(1.22)^4 ≈ 775.37 → 775
x = 5: 350(1.22)^5 ≈ 945.95 → 946

The correct graph is the increasing curve with x from 0 to 10 and y up to 2000 (the third graph), since the population grows exponentially above 350 and reaches values near the ones listed above.