Answer:
a) [tex]500=(1+r)^{40}[/tex]
b) 16.81%
Step-by-step explanation:
a)
The general formula for compound growth is:
[tex]F=P(1+r)^t[/tex]
Where
F is the future amount (5000 in our case)
P is the present amount (10 here)
r is the rate of growth (we don't know that yet)
t is the time in years (that would be 1980 - 1940 = 40)
So, the formula becomes:
[tex]F=P(1+r)^t\\5000=10(1+r)^{40}\\500=(1+r)^{40}[/tex]
b)
We need to find the growth rate (annual percentage increase). So we have to solve for "r" in the equation found in part (a).
[tex]500=(1+r)^{40}\\\sqrt[40]{500} =\sqrt[40]{(1+r)^{40}} \\1.1681=1+r\\r = 1.1681 - 1 = 0.1681[/tex]
To get percentage, we multiply by 100:
0.1681 * 100 = 16.81%
