Question

2.) the equation $p = 1,800 \cdot 0.97^t$ gives the expected population ($p$) of an endangered bird species $t$ years from now.
in this situation,

• the number 1,800 represents the:

a. decay factor
b. growth factor
c. bird species population now
d. bird species population $t$ years from now

• the number 0.97 represents the:

a. decay factor
b. growth factor
c. bird species population now
d. bird species population $t$ years from now

Explanation:

For the first sub - question (about 1,800):

Step1: Recall the exponential decay formula

The general form of an exponential decay function is $p = a\cdot b^{t}$, where $a$ is the initial amount, $b$ is the decay factor (with $0 < b< 1$), and $t$ is time.

Step2: Analyze the given equation $p = 1800\cdot0.97^{t}$

When $t = 0$ (representing "now"), we substitute $t = 0$ into the equation: $p=1800\times0.97^{0}=1800\times1 = 1800$. So 1800 represents the population of the bird species now.

For the second sub - question (about 0.97):

Step1: Recall the exponential decay formula

In the exponential decay function $p = a\cdot b^{t}$, $b$ is the decay factor when $0 < b< 1$.

Step2: Analyze the value 0.97

Since $0.97<1$, in the equation $p = 1800\cdot0.97^{t}$, 0.97 is the decay factor.

Answer:

For the first sub - question: C. Bird species population now
For the second sub - question: A. Decay Factor