Final answer:
The initial amount is 25 and the rate of growth is 120%. The function will evaluate to approximately 77.7 when t = 5.
Step-by-step explanation:
The exponential function given is: y = 25(1.2)^t, where y represents the value, t represents time, and 25 is the initial amount. The rate of growth is represented by the base, 1.2, raised to the power of t.
To identify the initial amount, we look at the equation when t = 0.
Substituting t = 0 in the equation, we get y = 25(1.2)^0 = 25.
Therefore, the initial amount is 25. The rate of growth, r, is represented by 1.2 as a percent.
To convert it to a percent, we multiply it by 100, so the rate of growth is 1.2 x 100 = 120%.
To evaluate the function when t = 5, we substitute t = 5 in the equation.
Evaluating this, we get y = 25(1.2)^5 ≈ 77.7.
Rounding this to the nearest tenth, the evaluated function when t = 5 is approximately 77.7.