1. Identify the initial amount a and the growth factor b in the exponential function.
f(t)=1.4^t
a. a=1, b=0.4
b. a=1.4, b=0
c. a=1.4, b=t
a. a=1, b=1.4
a. a=1, b=1.4
The correct answer is a. a=1, b=0.4.
In the exponential function f(t) = 1.4^t, the initial amount (a) is 1, and the growth factor (b) is 0.4. The base of the exponentiation is 1.4.
To identify the initial amount (a) and the growth factor (b) in the exponential function f(t)=1.4^t, we need to understand their meanings.
The initial amount (a) represents the value of the function when the input (t) is zero. In this case, when t=0, we have f(0)=1.4^0=1. This means that a=1.
The growth factor (b) gives us information about how much the function grows or decays with each unit increase in the input. It is determined by the base of the exponent. In this case, the base is 1.4, which means that for every unit increase in t, the function is multiplied by 1.4. Therefore, b=0.4.
Hence, the correct answer is a: a=1, b=0.4.