Initial amount = 1
Rate of growth = 80 %
The value is 18.9 when t = 5
Solution:
The given exponential function is:
[tex]y = a(1+r)^t[/tex]
Where,
y is the future value
a is the initial value
r is the growth rate
t is the number of years
Compare both the functions,
a = 1
[tex]1+r = 1.8\\\\r = 1.8 - 1\\\\r = 0.8[/tex]
Thus growth rate is:
[tex]r = 0.8 = 0.8 \times 100 \% = 80 \%[/tex]
Evaluate the function when t = 5
Substitute t = 5 in given
[tex]p(5) = 1.8^5\\\\p(5) = 18.89568 \approx 18.9[/tex]
Thus the value is 18.9 when t = 5
