Question

A company makes a donation to charity every year.The value of the donation increases exponentially by 10%. The value of the donation in 2010 was $10000. a)Find the value of the donation in2016. b)Find the total value of the donations made during the year 2010 to 2016 , Inclusive​ Just answer both questions properly or do not answer

Answer 1

Given :-

• A company makes a donation to charity every year.
• The value of the donation increases exponentially by 10%.
• The value of the donation in 2010 was $10000.

To Find :-

• The value of the donation in 2016. ?
• The total value of the donations made during the year 2010 to 2016 . ?

Formula used :-

• Final value = initial value * [ 1 + (increase per year %/100) ] ^ (Time interval)

Solution :-

From given data we have :-

• initial value of Donation in 2010 = $10000.
• increase per year = 10% .
• Time interval = 2016 - 2010 = 6 years.

Putting all values in formula now, we get,

→ Final value = 10000 * [ 1 + (10/100) ]⁶

→ Final value = 10000 * [ 1 + (1/10) ]⁶

→ Final value = 10000 * (11/10)⁶

→ Final value = 10000 * (11)⁶ / (1000000)

→ Final value = 11⁶ / 100

→ Final value = (1771561/100)

→ Final value = $17715.61. (Ans.)

Therefore, The value of the donation in 2016 is $17715.61.

Hence,

→ The total value of the donations made during the year 2010 to 2016 = 17715.61 - 10000 = $7715.61 (Ans.)

Answer 2

Given :-

• A company makes a donation to charity every year.
• The value of the donation increases exponentially by 10%
• The value of the donation in 2010 was $10000.

To Find :-

• The value of the donation in 2016
• The total value of the donations made during the year 2010 to 2016

Solution :-

First of all, we need to find the value of the donation in 2016

We have,

• The donation increases exponentially by 10%
• Initial Value of domination in 2010 is $1000
• Time Interval is 6 years

We know that,

$\sf Final \: Value = Initial \: Value [ \frac{1 + Increase \: per \: year \: \%}{100}]^{Time \: Interval}$

Substituting the give values we get,

$:\implies\sf Final \: Value = 10000 [1 + \frac{1\cancel0}{10\cancel0}]^{6}$

$:\implies\sf Final \: Value = 10000 [1 + \frac{1}{10}]^{6}$

$:\implies\sf Final\:Value = 10000 \: (\frac{11}{10})^{6}$

$:\implies\sf Final \: Value = 1\cancel{0000} [\frac{11^{6}} {100\cancel{0000}}]$

$:\implies\sf Final \: Value = \frac{11^{6}}{100}$

$:\implies\sf Final\:Value = \frac{\cancel{1771561}}{\cancel{100}}$

$:\implies\sf Final\:Value = \ 17715.61$

Therefore, the value of the donation in 2016 is $ 17715.61

Then, we need to find the total value of the donations made during the year 2010 to 2016

Hence, the total value of the donations made during the year 2010 to 2016 is 17715.61 - 10000 = $7715.61