# a website has 500,000 members in 2010. The number of members increases by 15% each year. Write an exponential growth function that represents the website membership t years after 2010. use the equation to find: how many members will there be in 2016. please help with both.

## M(t) = 500000*1.15^t

Now just find M(6)

although, technically, M(6) is the number of members at the end of 2016...

## To represent the exponential growth of the website membership t years after 2010, we can use the formula:

N(t) = N₀ × (1 + r)^t

Where:
N(t) represents the number of members after t years,
N₀ represents the initial number of members (in 2010), which is 500,000,
r represents the growth rate as a decimal, which is 15% or 0.15,
t represents the number of years after 2010.

Substituting the values into the equation, we get:

N(t) = 500,000 × (1 + 0.15)^t

To find the number of members in 2016, we need to substitute t = 6 into the equation since 2016 is 6 years after 2010:

N(2016) = 500,000 × (1 + 0.15)^6

Simplifying the equation, we have:

N(2016) = 500,000 × (1.15)^6

Now, let's calculate it:

N(2016) = 500,000 × (1.15)^6
N(2016) = 500,000 × 2.078

Therefore, there will be approximately 1,039,000 members on the website in 2016.

## To write an exponential growth function that represents the website membership t years after 2010, we can use the formula:

N(t) = N₀ * (1 + r)^t

Where:
N(t) = the number of members t years after 2010
N₀ = the initial number of members in 2010 (500,000 in this case)
r = the growth rate (expressed as a decimal)
t = the number of years after 2010

In this case, the growth rate is 15%, which can be written as a decimal as 0.15.

Therefore, the exponential growth function for this scenario is:

N(t) = 500,000 * (1 + 0.15)^t

Now, let's use this equation to find the number of members in 2016 (6 years after 2010):

t = 2016 - 2010 = 6

Plugging this value into the equation:

N(6) = 500,000 * (1 + 0.15)^6

Calculating the result:

N(6) = 500,000 * (1.15)^6

N(6) ≈ 830,045

Therefore, there will be approximately 830,045 members in the website in 2016.