Use the properties of exponents to rewrite the exponential function y=750(1.6)t4 in the form y=a(1+r)x .Select the correct answers from the lists.(1 point)The function is at a constant percent rate of change of about %.

Answer 1

To rewrite the function \( y = 750(1.6)^{t^4} \) in the form \( y = a(1 + r)^x \), we need to express it appropriately. The key distinction here is to identify what \( x \) will be.

1. First, we can rewrite the term \( (1.6)^{t^4} \). We know that: \[ 1.6 = 1 + 0.6 \] Thus, we can write: \[ (1.6)^{t^4} = (1 + 0.6)^{t^4} \]

2. So, we can replace \( (1.6)^{t^4} \) with \( (1 + 0.6)^{t^4} \) while keeping \( 750 \) as the initial amount \( a \): \[ y = 750(1 + 0.6)^{t^4} \]

3. In this case, we see that \( a = 750 \), \( r = 0.6 \), and the exponent \( x \) is \( t^4 \).

Now, to express the percentage rate of change:

4. The change rate \( r \) in percentage form is found by multiplying \( r \) by 100: \[ r = 0.6 \implies \text{Percentage Rate} = 0.6 \times 100 = 60% \]

In conclusion, the function is in the form \( y = 750(1 + 0.6)^{t^4} \) and it has a constant percent rate of change of about 60%.

So, the final answers are:

• \( a = 750 \)
• \( r = 0.6 \)
• Constant percent rate of change: 60%.