Answer: a). $17,715.61.
b). $95,872.61.
Step-by-step explanation:
a). Let's denote the initial value of the donation in 2010 as V₀ = $10,000 and the annual increase as 10% or 0.10.
The value of the donation in 2016 (V₆) can be calculated using the formula for exponential growth:
Vₙ = V₀ * (1 + r)^n
Where:
Vₙ = value of the donation after n years
V₀ = initial value of the donation (in 2010)
r = annual growth rate (in this case, 10% or 0.10)
n = number of years
V₆ = $10,000 * (1 + 0.10)^6
V₆ = $10,000 * 1.10^6
V₆ ≈ $10,000 * 1.771561
V₆ ≈ $17,715.61
So, the value of the donation in 2016 is approximately $17,715.61.
b). To find the total value of the donations made during the years 2010 to 2016 (inclusive), we need to sum up the values of the donations for each year from 2010 to 2016.
The total value of the donations is given by:
Total Value = V₀ + V₁ + V₂ + ... + V₆
We already know the value of the donation in 2010 (V₀ = $10,000), and we have calculated the value of the donation in 2016 (V₆ ≈ $17,715.61).
Now, let's calculate the values of the donations for the years 2011 to 2015:
V₁ = V₀ * (1 + r) = $10,000 * 1.10 ≈ $11,000
V₂ = V₁ * (1 + r) = $11,000 * 1.10 ≈ $12,100
V₃ = V₂ * (1 + r) = $12,100 * 1.10 ≈ $13,310
V₄ = V₃ * (1 + r) = $13,310 * 1.10 ≈ $14,641
V₅ = V₄ * (1 + r) = $14,641 * 1.10 ≈ $16,105
V₆ (already calculated) ≈ $17,715.61
Now, let's sum up all the values:
Total Value = $10,000 + $11,000 + $12,100 + $13,310 + $14,641 + $16,105 + $17,715.61
Total Value ≈ $95,872.61
The total value of the donations made during the years 2010 to 2016, inclusive, is approximately $95,872.61.