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.

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.