# 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

Question
Exponential growth and decay
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

2021-02-22
We have to find formula for f if growth rate is 2% and f(0)=147
Definition of exponential function:
An exponential growth or decay function is the function which grows or shri
at some condition of growth percentage,
so equation of exponential function can be expressed as:
$$f(x)=a(1+r)^x or f(x)=ab^x$$ (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,
$$f(t)=ab^t$$
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=a*1
a=147
$$(since, (any finite number)^0=1)$$
After putting value of a we can write the formula for f,
$$f(t)=147(1.02)^t$$
Hence, option c) is correct.

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