Question

Suppose f is an exponential function and:

Answer 1

Answer:  a) $b= p(1 + r)^1$ b) $c= p(1 + r)^n$ c) $d= p(1 + r)^m$ d) $b^n=c$

Step-by-step explanation:

Since f is an exponential function.

So, it is expressed as

$f = p(1 + r)^$

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.

$b= p(1 + r)^1$

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

$c= p(1 + r)^n$

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

$d= p(1 + r)^m$

Write a formula that expresses c in terms of b.

Since

$b=p(1+r)^1\\\\So,\\\\b=p(1+r)^{n\times \frac{1}{n}}\\\\b=(p(1+r)^n)^{\frac{1}{n}}\\\\b=c^{\frac{1}{n}}\\\\b^n=c$

Hence, a) $b= p(1 + r)^1$ b) $c= p(1 + r)^n$ c) $d= p(1 + r)^m$ d) $b^n=c$