Question

put the following into the form $y = ab^x + c$:\

1. $y = 4(3)^{2x + 1} - 7$\
2. $y = 2(2)^{3(x + 2)} - 1$

Explanation:

Step1: Rewrite exponent using rule $a^{m+n}=a^m a^n$

$y = 4(3)^{2x+1}-7 = 4\cdot 3^{2x}\cdot 3^1 -7$

Step2: Simplify coefficient and rewrite $3^{2x}$

$y = 12\cdot (3^2)^x -7 = 12\cdot 9^x -7$
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Step1: Rewrite exponent using rule $a^{m(n+p)}=a^{mn+mp}$

$y = 2(2)^{3(x+2)}-1 = 2(2)^{3x+6}-1$

Step2: Split exponent using $a^{m+n}=a^m a^n$

$y = 2\cdot 2^{3x}\cdot 2^6 -1$

Step3: Calculate coefficient and rewrite $2^{3x}$

$y = 2\cdot 64\cdot (2^3)^x -1 = 128\cdot 8^x -1$

Answer:

1. $y = 12\cdot 9^x -7$
2. $y = 128\cdot 8^x -1$