Question

sec 6.1 exponential functions: problem 6
(1 point)
consider the equation ( y = 174(1.48)^{x} ), which is of the form ( y = ab^{x} ), to fill in the following blanks.
the initial value for equation is . the base, denoted by ( b ), for the equation is . therefore, the type of change represented is because
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Explanation:

Step1: Identify the initial value

In the exponential function \(y = ab^{x}\), when \(x = 0\), \(y=a\). For \(y = 174(1.48)^{x}\), when \(x = 0\), \(y=174\times(1.48)^{0}=174\times1 = 174\).

Step2: Identify the base

Comparing \(y = 174(1.48)^{x}\) with \(y = ab^{x}\), the base \(b = 1.48\).

Step3: Determine the type of change

Since \(b=1.48> 1\), the function represents exponential growth.

Answer:

The initial value for the equation is \(174\). The base, denoted by \(b\), for the equation is \(1.48\). Therefore, the type of change represented is exponential growth because \(b = 1.48>1\).