nls模型中^和exp（）表示法的区别

Question

我想了解nls模型中^和exp（）表示法的区别。在我的示例中：

library(nls2)
#Data set
x <- c(1 ,10,  20,  30,  40,  50,  60,  70,  80,  90, 100) 
y <- c(0.033823,  0.014779,  0.004698,  0.001584, -0.002017, -0.003436, 
-0.000006, -0.004626, -0.004626, -0.004626, -0.004626) 

带有exp（）的NLS

fo2<- y ~ a4^(-x/a5)
fm2 <- nls2(fo2, alg = "plinear-random",
     start = data.frame(a4 = c(-10, 10), a5 = c(-10, 10)),
     control = nls.control(maxiter = 1000))

带有^

的NLS

fo3<- y ~ a4*exp(-x/a5)
fm3 <- nls2(fo3, alg = "plinear-random",
     start = data.frame(a4 = c(-10, 10), a5 = c(-10, 10)),
     control = nls.control(maxiter = 1000))

结果

summary(fm2)

Formula: y ~ a4^(-x/a5)

Parameters:
      Estimate Std. Error t value Pr(>|t|)    
a4   1.346e+00  3.060e+06     0.0        1    
a5   2.890e+00  5.103e-03   566.4   <2e-16 ***
.lin 3.790e-02  2.211e+07     0.0        1    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.003675 on 8 degrees of freedom

Number of iterations to convergence: 1000 
Achieved convergence tolerance: NA

summary(fm3)

Formula: y ~ a4 * exp(-x/a5)

Parameters:
      Estimate Std. Error t value Pr(>|t|)   
a4   5.456e+00  1.474e+09   0.000  1.00000   
a5   9.764e+00  2.294e+00   4.256  0.00278 **
.lin 6.940e-03  1.875e+06   0.000  1.00000   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.003675 on 8 degrees of freedom

Number of iterations to convergence: 1000 
Achieved convergence tolerance: NA

我的输出太含糊。任何成员都可以简单地解释不同的方法吗？谢谢，