Question

e of tasmanian wolf t years after 1900. graph the exponential unding to the nearest integer whenever necessary. population size of tasmanian wolf 187 161 138 119 102 00 where t = 0 the input t represents years after 1900, and the output is the population. for example, year 1900 means t = 0. what would be the coordinates for that first point? ask the ai coach a question

Explanation:

Step1: Identify t and population at t=0

Given \( t \) is years after 1900, so at 1900, \( t = 0 \). We need the population at \( t = 0 \). From the table (assuming the first entry is for \( t = 0 \), but looking at the context, when \( t = 0 \) (year 1900), we need to find the population. Wait, maybe the table has values, but the key is: input \( t \), output population. So for \( t = 0 \) (1900), we need the population value. Let's check the table: the first row (maybe) has population? Wait, the text says "year 1900 means \( t = 0 \)". So we need to find the population when \( t = 0 \). Looking at the table, maybe the first entry (but the table is a bit unclear, but the key is: coordinate is \( (t, \text{population}) \). So \( t = 0 \), and we need the population at \( t = 0 \). Let's assume that when \( t = 0 \) (1900), the population is, say, from the table, maybe the first value? Wait, the user's table: "population size of tasmanian wolf" with values 187, 161, 138, 119, 102. Wait, maybe the first value (187) is for \( t = 0 \)? Wait, no, maybe the years: if \( t = 0 \) is 1900, then we need to find the population at \( t = 0 \). Let's re-express: the input is \( t \) (years after 1900), output is population. So coordinate is \( (t, P(t)) \), where \( P(t) \) is population. For the first point (year 1900, \( t = 0 \)), we need \( P(0) \). Let's say that from the table, when \( t = 0 \), the population is, let's check the table. Wait, the table has "00 where \( t = 0 \)" at the bottom? Wait, the user's image: "00 where \( t = 0 \)" maybe indicating that at \( t = 0 \) (1900), the population is, let's see the table. Wait, the first population value is 187. So if \( t = 0 \), then the coordinate is \( (0, 187) \)? Wait, maybe. Let's confirm: \( t = 0 \) (input), population (output) is 187 (assuming the first row is \( t = 0 \)). So the coordinate is \( (0, 187) \).

Step2: Form the coordinate

Since \( t = 0 \) (input) and population (output) is, say, 187 (from the table's first value), the coordinate is \( (0, 187) \). Wait, but let's check again. The problem says "the first point" which is \( t = 0 \) (year 1900). So we need to find \( P(0) \), the population at \( t = 0 \). From the table, the population values are 187, 161, 138, 119, 102. Maybe these are for \( t = 0, 1, 2, 3, 4 \)? So \( t = 0 \) → 187, \( t = 1 \) → 161, etc. So the first point ( \( t = 0 \)) has coordinate \( (0, 187) \).

Answer:

The coordinate for the first point (year 1900, \( t = 0 \)) is \(\boxed{(0, 187)}\) (assuming the first population value is for \( t = 0 \); adjust if the table's first value corresponds to \( t = 0 \)).