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

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:
$f(x)=a(1+r{)}^{x}orf(x)=a{b}^x$ (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,
$r=2\mathrm{\%}$
=$2/100$)
$=0.02$
so,
$b=1+r$
$=1+0.02$
$=1.02$
Step 2
Taking variable as t,
$f(t)=a{b}^t$
Therefore,
$f(t)=abt=a(1.02{)}^t$
Given, $f(0)=147$
putting $t=0$, we get
$f(t)=a(1.02{)}^t$
$f(0)=a(1.02{)}^0$
$147=a\cdot 1$
$a=147$
${\text{(since, (any finite number)}}^0=1)$
After putting value of a we can write the formula for f,
$f(t)=147(1.02{)}^t$
Hence, option c) is correct.