Identify the initial amount a and the growth factor b in the exponential function g(x) = 14 × 2^x

Solution:

Given,

g(x) = 14 × 2^x

It is an exponential function.

y = ab^x

where a is the initial amount and b is the growth/ decay factor.

Now we will compare the given function with ab^x

And 14 × 2^x

A = 14

B = 2

Therefore, the initial amount a is 14 and the growth factor b is 2

Example:

Identify the initial amount a and the growth factor b in the exponential function g(x) = 24 × 4^x

Solution:

Given,

g(x) = 24 × 4^x

It is an exponential function.

y = ab^x

where, a is the initial amount and b is the growth/ decay factor.

Now we will compare the given function with ab^x

And 24 × 4^x

A = 24

B = 4

Therefore, the initial amount a is 24 and the growth factor b is 4.

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Identify the initial amount a and the growth factor b in the exponential function g(x) = 14 × 2^x

Summary:

The initial amount a and the growth factor b in the exponential function g(x) = 14 × 2^x is 14 and 2 respectively.