Question

the global population of a specific breed of trees, after t decades, is given by the function $p(t) = 5t^5 - 2t^2 + 2911$. what is the population of trees after $t = 7$ decades?
show your work here

Explanation:

Step1: Substitute t = 7 into the function

We have the function \( p(t)=5t^{5}-2t^{2}+2911 \). Substitute \( t = 7 \) into it:
\( p(7)=5\times7^{5}-2\times7^{2}+2911 \)

Step2: Calculate each term

First, calculate \( 7^{5} \): \( 7^{5}=7\times7\times7\times7\times7 = 16807 \)
Then, \( 5\times7^{5}=5\times16807 = 84035 \)
Next, calculate \( 7^{2}=49 \), so \( 2\times7^{2}=2\times49 = 98 \)

Step3: Combine the terms

Now, substitute these values back into the expression for \( p(7) \):
\( p(7)=84035 - 98+2911 \)
First, \( 84035-98 = 83937 \)
Then, \( 83937+2911 = 86848 \)

Answer:

The population of trees after \( t = 7 \) decades is \( 86848 \).