Question

scientists collected monthly data on the population of beetles and geckos in a portion of the rainforest. the results are shown in the table.

# of geckos	41	24	10	92	156	50	72

statement: the function y = 0.13x + 1.1 can be used to model the data.

if a scientist found 35 geckos, she would estimate the beetle population to be about 277.

if the beetle population is 1,500, scientists could predict finding about 196 geckos.

rewrite the false statement to make it true

Explanation:

Step1: Use the given linear - function formula

The function is $y = 0.13x+1.1$, where $y$ is the beetle population and $x$ is the gecko population.

Step2: Substitute $x = 35$ into the function

When $x = 35$, we calculate $y$ as follows: $y=0.13\times35 + 1.1$. First, $0.13\times35=4.55$. Then $y=4.55 + 1.1=5.65$. This is wrong. The correct way is to use the linear - function relationship. If $x = 35$, then $y=0.13\times35+1.1=4.55 + 1.1 = 5.65$. But if we assume the relationship holds, when $x = 35$, $y=0.13\times35+1.1 = 4.55+1.1=5.65$ is wrong. The correct calculation: $y = 0.13x+1.1$, substituting $x = 35$ gives $y=0.13\times35 + 1.1=4.55+1.1 = 5.65$. The statement about $y = 277$ is false.
To correct the second statement: If the beetle population is 1500, we set $y = 1500$ in the equation $y=0.13x + 1.1$ and solve for $x$.
$1500=0.13x+1.1$.
Subtract 1.1 from both sides: $1500 - 1.1=0.13x$, so $1498.9 = 0.13x$.
Then $x=\frac{1498.9}{0.13}\approx11530$ geckos.
To correct the third statement:
The function $y = 0.13x+1.1$ is used to model the relationship between the number of geckos ($x$) and the number of beetles ($y$).

Answer:

If the beetle population is 1500, scientists could predict finding about 11530 geckos.
If a scientist found 35 geckos, she would estimate the beetle population to be $y=0.13\times35 + 1.1=4.55+1.1 = 5.65$ (assuming the model is valid for this input). The function $y = 0.13x+1.1$ can be used to model the data.