The requirement for computer server capacity at Acme Industries is expected to increase at a rate of 15% per year for the next 5 years. If the server capacity is expected to be 1,400 gigabytes in 5 years, how many gigabytes of capacity are there today? Round to the nearest whole gigabyte.
C = Co + Co*r*t = 1400 Gigabytes.
Co + Co*0.15*5 = 1400
Co + 0.75Co = 1400
1.75Co = 1400
Co = 800 Gigabytes = Today's capacity.
To find the current server capacity, we need to calculate the present value of the future capacity using the given growth rate.
Let's assume the current server capacity is represented by C gigabytes. The future capacity in 5 years will be 1,400 gigabytes, so we have:
C * (1 + 0.15)^5 = 1,400
Simplifying the equation, we have:
1.15^5 * C = 1,400
Taking the value of 1.15 raised to the power of 5, we get approximately 1.869
1.869 * C = 1,400
Now, divide both sides of the equation by 1.869 to isolate C:
C = 1,400 / 1.869
C ≈ 747.88
Rounding to the nearest whole gigabyte, the current server capacity is approximately 748 gigabytes.
To solve this problem, we can use the concept of exponential growth.
The formula for calculating exponential growth is:
A = P * (1 + r)^t
Where:
A = Final amount (in this case, the server capacity in 5 years)
P = Initial amount (the current server capacity)
r = Rate of growth as a decimal (in this case, 15% = 0.15)
t = Time in years (in this case, 5 years)
We can rearrange the formula to solve for the initial amount (P):
P = A / (1 + r)^t
Now we can plug in the values provided and calculate the initial capacity:
A = 1,400 gigabytes (the server capacity in 5 years)
r = 0.15 (15% growth rate per year)
t = 5 years
P = 1,400 / (1 + 0.15)^5
Calculating this:
P = 1,400 / (1.15)^5
P ≈ 823.7
Therefore, the current server capacity is approximately 824 gigabytes.