Question

Akiba started studying how the number of branches on his tree changes over time. The relationship between the elapsed time, t tt, in years, since Akiba started studying his tree, and the total number of its branches, N ( t ) N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function:

Answer 1

75% added too

Explanation:

Answer 2

Complete the Statement:

Every Year, ____% of Branches are [added to/subtracted from] the Total Number of Branches

Answer:

• 75%
• Added To

Explanation:

The relationship between the elapsed time, t, in years, since Akiba started studying his tree, and the total number of its branches,N(t)is modeled by the following function:
`N(t)=42\cdot 1.75^t`

If we look at the growth function, we can re-write N(t) below:

`N(t)=42\cdot 1.75^t\\=42(1+0.75)^t\\=42(1+(75)/(100) )^t\\N(t)=42(1+75\% )^t`

We can see the following:

• Akiba's Tree initially had 42 Branches
• The number of branches grew by 75% each year, therefore 75% of branches are added to the total number of branches.