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Suppose f is an exponential function and:
(a) b represents the 1-unit growth factor for f.
(b) c represents the n n-unit growth factor for f.
(c) d represents the m m-unit growth factor for f.

Write a formula that expresses c in terms of b.

Answer :

Answer:  a) [tex]b= p(1 + r)^1[/tex] b) [tex]c= p(1 + r)^n[/tex] c) [tex]d= p(1 + r)^m[/tex] d) [tex]b^n=c[/tex]

Step-by-step explanation:

Since f is an exponential function.

So, it is expressed as

[tex]f = p(1 + r)^[/tex]

Here f is the present value

p is the initial value

r is the rate of growth per time period

t is the time period.

(a) b represents the 1-unit growth factor for f.

[tex]b= p(1 + r)^1[/tex]

(b) c represents the n n-unit growth factor for f.

[tex]c= p(1 + r)^n[/tex]

(c) d represents the m m-unit growth factor for f.

[tex]d= p(1 + r)^m[/tex]

Write a formula that expresses c in terms of b.

Since

[tex]b=p(1+r)^1\\\\So,\\\\b=p(1+r)^{n\times \frac{1}{n}}\\\\b=(p(1+r)^n)^{\frac{1}{n}}\\\\b=c^{\frac{1}{n}}\\\\b^n=c[/tex]

Hence, a) [tex]b= p(1 + r)^1[/tex] b) [tex]c= p(1 + r)^n[/tex] c) [tex]d= p(1 + r)^m[/tex] d) [tex]b^n=c[/tex]

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