Identify the initial amount "a" and the rate of growth "r" (as a percent) of the exponential function. Evaluate the function when t = 5. Round your answer to the nearest tenth

Question

What will be an ideal response?

Answer 1

Answer:
Initial amount = 1
Rate of growth = 80 %
The value is 18.9 when t = 5
Solution:
The given exponential function is:
p(t) = 1.8^t
The exponential function is given as:
y = a(1+r)^t
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
1+r = 1.8
r = 1.8 - 1
r = 0.8
Thus growth rate is:
r = 0.8 = 0.8 \times 100 \% = 80 \%
Evaluate the function when t = 5
Substitute t = 5 in given
p(5) = 1.8^5
p(5) = 18.89568 approx 18.9
Thus the value is 18.9 when t = 5