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 2021-02-21 Answered

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

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Expert Answer

Alannej
Answered 2021-02-22 Author has 104 answers

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)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)
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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