Question

a disease - causing fungus was introduced to a plant population. the equation n = 3^t describes the number of infected plants t days after the fungus was introduced. how many days will it take for the number of infected plants to reach 81?

Explanation:

Step1: Set up the equation

We are given the equation $N = 3^{t}$, and we want to find $t$ when $N = 81$. So we set up the equation $81=3^{t}$.

Step2: Rewrite 81 as a power of 3

Since $81 = 3\times3\times3\times3=3^{4}$, the equation $81 = 3^{t}$ becomes $3^{4}=3^{t}$.

Step3: Solve for t

If $a^{m}=a^{n}$, then $m = n$ for $a>0,a
eq1$. Here $a = 3$, so $t = 4$.

Answer:

4