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a stretch by a factor of 2 for the exponential growth function f(x)= a(9/4) occurs when a = 1/2, 1, 2, or 9/4

a stretch by a factor of 11/3 for the exponential decay function f(x)= a(3/5) occurs when a = 1/3, 3/5, 1, or 11/3

a shrink by a factor of 1/3 for the exponential growth function f(x)= a(7)^x occurs when a = 1/3, 1, 7/3, or 7

a shrink by a factor of 2/5 for the exponential decay function f(x)= a(2/9)^x occurs when a = 1/5, 2/5, 2/9, or 5/2

Remember that stretching or compressing the graph of a function is a transformation in which you multiply the whole function by a constant . If , you are compressing the graph of the function by a factor of . If , you are stretching the graph of the function by a factor of .

1. Here we want to stretch the graph by a factor of 2. Since 2 > 1, we just need to multiply the whole function by 2. Therefore, A stretch by a factor of 2 for the exponential growth function f(x)= a(9/4) occurs when a =2.

2. Here we want to stretch the graph by a factor of 11/3. Since 11/3 > 1, we just need to multiply the whole function by 11/3. Therefore, a stretch by a factor of 11/3 for the exponential decay function f(x)= a(3/5) occurs when a=11/3.

3. Here we want to compress the graph by a factor of 1/3, so . The only number in our options that satisfy that condition is 1/3. Therefore, a shrink by a factor of 1/3 for the exponential growth function f(x)= a(7)^x occurs when a = 1/3.

4. Here we want to compress the graph by a factor of 2/5, so . since 0<2.5<1, we just need to multiply the whole function by 2/5. Therefore, A shrink by a factor of 2/5 for the exponential decay function f(x)= a(2/9)^x occurs when a =2/5.