Questions: Test 4 - Chapter 4 Score: 0/17 Answered: 0/17 Question 1 A population numbers 16,000 organisms initially and grows by 1.4% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P=ab^t, where P=

Test 4 - Chapter 4 Score: 0/17 Answered: 0/17

Question 1

A population numbers 16,000 organisms initially and grows by 1.4% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P=ab^t, where P=

Transcript text: Test 4 - Chapter 4 Score: 0/17 Answered: 0/17 Question 1 A population numbers 16,000 organisms initially and grows by $1.4 \%$ each year. Suppose $P$ represents population and $t$ represents the number of years of growth. An exponential model for the population can be written in the form $P=a b^{t}$, where $P=$ $\square$ Submit Question

Solution

Solution Steps

Step 1: Identify the Initial Population Size

The initial population size, $P_0$, is given as 16000.

Step 2: Determine the Annual Growth Rate

The annual growth rate, $r$, is given as 1.4. After converting to a decimal, it becomes 0.014.

Step 3: Calculate the Growth Factor

The growth factor, $b$, is calculated using the formula $b = 1 + r$. Substituting the given rate, we get $b = 1 + 0.014 = 1.014$.

Step 4: Calculate the Population at Time $t$

Using the exponential growth formula $P(t) = P_0 \cdot b^t\ = 16000 \cdot 1.014^t $, and substituting $P_0 = 16000$, $b = 1.014$, and $t = 1$, we get $P(t) = 16000 \cdot 1.014^1 = 16224$.