Suppose that  f  is an exponential function with a percentage growth rate of  2% , and with f(0)=147. Find a formula for  f .a) f(t)=0.02t+147b) f(t)=1.02(1.47)tc) f(t)=147(1.02)td) f(t)=147(2)te) f(t)=147(1.20)t

Falak Kinney

Falak Kinney

Answered question

2021-02-21

Suppose that  f  is an exponential function with a percentage growth rate of  2% , and with f(0)=147. Find a formula for  f .
a) f(t)=0.02t+147
b) f(t)=1.02(1.47)t
c) f(t)=147(1.02)t
d) f(t)=147(2)t
e) f(t)=147(1.20)t

Answer & Explanation

Alannej

Alannej

Skilled2021-02-22Added 104 answers

We have to find formula for f if growth rate is 2% and f(0)=147
The exponential function is defined as:
The function that increases or decreases at a certain growth percentage condition is known as an exponential growth or decay function.
Consequently, the exponential function equation can be written as:
f(x)=a(1+r)xorf(x)=abx (took b=1+r)
Here,
a is the initial value
r is the growth or decay rate written in decimal
b is the factor of growth or decay
According to question,
r=2%
=2/100)
=0.02
so,
b=1+r
=1+0.02
=1.02
Step 2
Taking variable as t,
f(t)=abt
Therefore,
f(t)=abt=a(1.02)t
Given, f(0)=147
putting t=0, we get
f(t)=a(1.02)t
f(0)=a(1.02)0
147=a1
a=147
(since, (any finite number)0=1)
We can write the formula for f after entering the value of a
f(t)=147(1.02)t
Hence, option c) is correct.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?